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NIELS BOHR BOOKS

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• 1 Introduction
• 2.1 Bohr's Assumptions
• 3.1.1 The Angular Momentum Quantum
• 3.1.2 Angular Momentum Is Quantized
• 3.1.3 Wavelengths
• 3.2 A Computational Model
• 4.2 Middling
• 4.3 Difficult
• 5 Connectedness
• 7 Shortcomings of the Bohr Model
• 8.1 Further Reading
• 8.2 External links
• 9 References

Introduction

This page gives basic information about the Bohr model of the atom and the quantization of electron angular momentum. These concepts are the basis of modern quantum physics and thus are essential to master before progressing to more complex quantum theories and principles. Although the Bohr model is regarded as inaccurate and outdated, the model predicts the hydrogen atom well and provides good predictions on quantized energy levels.

The Bohr Model was proposed in 1913 by the physicist Niels Bohr and is a description of the structure of atoms in which there is a dense positive core surrounded by orbiting electrons. In this model, the electrons orbit the nucleus in circular orbits, accounting for the series of discrete wavelengths in the H2 emission spectrum. Bohr's model of the hydrogen atom was the first to incorporate quantum theory, and the key idea of his model was that electrons occupy discrete orbitals.

The Bohr model of the atom was proposed by Niels Bohr in 1913 as an expansion on and correction of the Rutherford model. His model depicted atoms as having negatively charged electrons which orbited a small, positively charged nuclei containing most of the atom's mass, as Rutherford had done. However, the Bohr Model's incorporation of quantum theory set it apart from other models. In this model, electrons can only exist in discrete energy levels, which are quantized. The electrons orbit the nucleus at energy levels increasing (n= 1,2,3 ..) with their distance from the nucleus. Similar to stepping up a staircase, these energy levels are quantized. This model is very simplistic and is useful in introducing students to quantum mechanics. It also provides a decent first-order approximation of more complicated theories. Although this model successfully predicts energy levels of the hydrogen atom, it has major shortcomings once expanded to other atoms and more complex real-world situations. For example, one of the weaknesses of his analysis was not offering a reason for why only certain energy levels or orbitals were allowed.

Bohr's Assumptions

• Electrons travel in a circular orbit around the nucleus, similar to how planets orbit around the sun. (This was Bohr's inspiration for the model, electrons orbiting the nucleus.) Holding these electrons in these orbits are electrostatic forces rather than gravity.
• The energy of orbiting electrons is negative, in order to free an electron from the atom's orbit you must bring its energy to 0.
• The energy of electrons is inversely related to their distance from the nucleus and which energy level they occupy at that distance. The further away from the electron, the more energy it has. (Electric Potential Energy) [math]\displaystyle{ U = ((k)q_{1}q_{2})/d }[/math] (With the k constant representing the electrostatic/Coulomb constant)
• When electrons gain or lose energy they jump from one orbit to another. The energy is quantized - the orbitals have discreet radii or exact distances from the nucleus where electrons are allowed to exist, which Bohr called "stationary orbits."
• When an excited electron returns back to its ground state, then it releases the energy that is absorbed, in the form of a photon. All photons are produced by an electron transitioning to a lower energy level, or smaller radius or becoming closer to the nucleus. Conversely, an input of energy is required to transition an electron to a higher energy level. This quantized energy - in both cases - is equal to the difference between the respective energies of the orbits.

Stairs are a great way to visualize quantized energy. When you're going upstairs, you can only be standing on the steps, and not anywhere in between the steps. Similarly, energy can only be absorbed or emitted in specific quanta. Energy is required to go up the stairs, and energy is gained when jumping down from one stair to the next (in the electron's case, this energy is released as a photon - sometimes as visible light!).

Application

A mathematical model, the angular momentum quantum.

[math]\displaystyle{ ħ = h/2π =1.05*10^{-34} J*s }[/math]

h is known as Planck's constant, which is a physical constant that is essential in quantum mechanical calculations.

Angular Momentum Is Quantized

Bohr assumed that electrons in orbit are only allowed very specific values for the magnitude of their angular momentum , specifically integer multiples of ħ given by:

[math]\displaystyle{ |\vec L_{trans,C}| = rp = Nħ }[/math]

L is the angular momentum of the electron, p is the Linear Momentum of the electron, r is the radius of the electron's orbit, and N is an integer (1,2,3, ...).

We can derive the equation for r, the allowed Bohr radii for electron orbits for hydrogen, which has one electron and one proton.

1) The Electric Force the proton exerts on the electron is calculated using: [math]\displaystyle{ F_{el} = {\frac{e^2}{4π ε_{0} r^2}} }[/math]

2) Applying concepts from the momentum principle and curving motion: [math]\displaystyle{ |F_{perpendicular}| = {\frac{|p| |v|}{r}} = {\frac{e^2}{4π ε_{0} r^2}} }[/math]

3) Substituting for the relation between momentum and velocity ( [math]\displaystyle{ v = {\frac{p} {m_{e}}} }[/math] ) where [math]\displaystyle{ m_{e} }[/math] is the mass of an electron: [math]\displaystyle{ {\frac{|p|}{r}} *{\frac{|p|}{m_{e}}} = {\frac{e^2}{4π ε_{0} r^2}} }[/math]

4) Substituting in Bohr's conditions for the magnitude of [math]\displaystyle{ p }[/math] : [math]\displaystyle{ {\frac{N^2 ħ^2}{m_{e}r^3}} = {\frac{e^2}{4π ε_{0} r^2}} }[/math]

5) Solving for the allowed radii [math]\displaystyle{ r = {\frac{4π ε_{0} ħ^2N^2}{m_{e}e^2}} }[/math] where N = 1,2,3,...

6) This result is often simplified to [math]\displaystyle{ r_{n} = a_{0}n^2 }[/math] where [math]\displaystyle{ a_{0} = {\frac{4π ε_{0}ħ^2}{m_{e}e^2}} = 0.0529 }[/math] nm and n = 1,2,3,...

Additionally, the formula for energy of hydrogen atom of different levels is also derived from this model, and is the formula most helpful for simple calculations involving quantum mechanics.

[math]\displaystyle{ E = K + U_{electromagnetic} }[/math]

1) [math]\displaystyle{ E = {\frac{mv^2}{2}} - {\frac{{\frac{1}{2}}*{\frac{1}{4π ε0}}*{\frac{me^2}{ħ}}}{N^2}} }[/math]

which simplifies to

2) [math]\displaystyle{ E = {\frac{13.6 eV}{N^2}} }[/math] where N = 1,2,3

Wavelengths

In the early 1900's, light had been observed to have the properties of both a particle and a wave. In 1924, Louis de Broglie , a French physicist, hypothesized all matter holds properties of waves in his thesis Recherches sur la théorie des quanta (Research on the Theory of the Quanta). According to de Broglie, there is an inverse relationship between momentum and wavelength.

The de Broglie relationship can tell us about the wavelength associated with the electron and can tell us the energy that will be released in photons, or particles of energy: [math]\displaystyle{ λ = \frac{h}{mv} }[/math] or [math]\displaystyle{ λ = \frac{h}{p} }[/math]

h is Planck's constant (6.63x10e-34 joules.sec), and v is the frequency or the velocity of the disturbance in the medium of propagation.

This equation is used to help derive the equation for the angular momentum of an electron in orbit [math]\displaystyle{ L = \frac{nh}{2π} }[/math]

Derivation of de Broglie's relationship:

E = energy, m = mass, c = speed of light,

Assuming that the two energies would be equal or in practical units:

1) [math]\displaystyle{ mc^2 = hv }[/math]

Since particles do not necessarily travel with the speed of light,

2) [math]\displaystyle{ mv^2 = hv = mv^2 = \frac{hv}{λ} }[/math] (using [math]\displaystyle{ hv = \frac{hc}{λ} }[/math] )

3) [math]\displaystyle{ λ = \frac{hv}{mv^2} = \frac{h}{mv} }[/math]

A Computational Model

In this visualization, an electron in orbit around a hydrogen nucleus progresses upwards though the available energy levels of the Bohr Model. The accompanying graph highlights the energy corresponding to each orbit with respect to the distance between the electron and the hydrogen nucleus. The greater the distance, the less negative the electron's energy and thus the less energy that must be added to free the electron from its orbit. To interact with this glowscript visualization of the Bohr Model, click here .

You will also find a graph of Total Energy (eV), Kinetic Energy, and Potential Energy, with each jump representing the electron transitioning to an orbit.

PhET additionally provides an effective "Models of the Hydrogen Atom" simulation that compares the various predictive models including the Bohr model. Further, it employs absorption and compares the models to the experimental results. The link is provided below for further evaluation.

https://phet.colorado.edu/sims/cheerpj/hydrogen-atom/latest/hydrogen-atom.html?simulation=hydrogen-atom

The images above are stills taken from the PhET simulation. As the electron absorbs energy, it will move to a higher orbit (energy level), and when it drops back to the steady-state, it releases photon(s).

Find the magnitude of the translational angular momentum of an electron when a hydrogen atom is in its 2nd excited state above the ground state.

We know that the only possible states of the hydrogen atom are those when the electron's translational angular momentum is an integer multiple of ħ. [math]\displaystyle{ |\vec L_{trans,c}| = Nħ }[/math] For the 2nd excited state, N = 3 Now just plug the numbers in [math]\displaystyle{ |\vec L_{trans,c}| = (3)(1.05*10^{-34} J*s) = 3.15*10^{-34} J*s }[/math]

[6]A hydrogen atom is in state N = 3. Assuming N = 1 is the lowest energy state, calculate the K+U (energy of electron) in electron volts for this atomic hydrogen energy state.

1) [math]\displaystyle{ E(3) = {\frac{-13.6 eV}{3^2}} }[/math] = -1.51 Joules

2) [math]\displaystyle{ E(1) = {\frac{-13.6 eV}{1^2}} }[/math] = -13.6 Joules

3) K+U (a sum of the kinetic energy and the potential electromagnetic energy of the photon) = energy of photon = [math]\displaystyle{ E(1) - E(3) = {\frac{-13.6 eV}{3^2}} - {\frac{-13.6 eV}{1^2}} }[/math] = 12.09 Joules

Below is the graph of E as the hydrogen atom goes from N = 3 to N = 1.

Hydrogen has been detected transitioning from the 101 st to the 100 th energy levels. What is the wavelength of the radiation emitted from this transition? Where in the electromagnetic spectrum is this emission?

To solve this problem, we first need to use formulas derived from Bohr Model of hydrogen atom. It is [math]\displaystyle{ E = {\frac{-13.6 eV}{N^2}} }[/math]

Then solve for the wavelength using formula from Electromagnetic Wave Theory.

This wavelength falls in the microwave portion of the electromagnetic spectrum.

Connectedness

1. I chose this topic because I have unintentional conducted research on it outside of a classroom environment that was driven by a question that I have asked myself for as long as I can remember: What is light? I couldn't touch it, I couldn't produce it myself, and I could not explain where light comes from. I am so thankful that I grew up in the time where a) I could hop on the internet to see if there was an answer to my question and b) that the answer exists. We know what light is: photons of a wavelength in the visible spectrum, and we know where light comes from: energy released by electrons dropping in levels of orbit. I loved the introductory internet research I did on this subject, and it introduced me to the bizarre world of quantum physics, which I continue to be puzzled by and curious about. I also chose this topic because of my admiration for the man behind it, Niels Bohr. He was a man on the cutting edge of science who pushed our understanding of the universe by leaps and bounds by unveiling aspects of the microscopic universe.

2. As an industrial engineering major, it is pretty difficult to quantify how a concept of physics, especially one as specific and complex as Bohr's atomic model, will directly connect to my major. This should not stop me from seeking knowledge about it to possess a more well rounded knowledge of the world. Still, it isn't hard to find applications. If I am working to optimize the production of a laser engraving facility, for example, having an understanding of the basic dynamics behind the lasers and machinery will help me to have a more level conversation with the engineers developing and maintaining the lasers, and will prevent any massive rifts of understanding between the engineering side of the facility with the men working on the business end of the operation.

3. The industrial application of the concepts covered on this page are enormous in today's day and age. We are in the midst of an energy revolution, with solar energy looking to replace fossil fuels as the primary source of energy to the world. Understanding the energy of photons and light waves emitted from the sun is essential to the ongoing process making solar energy a more cost effective alternative to traditional fossil fuels. Once this optimization occurs, the planet will have a new primary source of energy with cleanliness and availability that is absolutely unprecedented.

To understand how revolutionary Bohr's theories and advancements were, one must have a general understanding of the accepted atomic model at the time, the Rutherford model. The Rutherford model was created in 1911 by New Zealand born chemist Ernest Rutherford . The dominant model for the structure of the atom before Rutherford's breakthrough, was the plum pudding model. While this model correctly surmised that atoms are constructed from constituents of both positive and negative charge and that the negatively charged components were quite small relative to the atom, the plum pudding model depicted electrons as stationary, lodged in place in a substance believed to constitute most of the space an atom occupies.

After conducting one of the most famous experiments in the world of physics, the Geiger-Marsden experiment , more commonly known as the gold foil experiment, Rutherford realized that the majority of the atom is empty space with the mass of the atom existing predominantly in a small volume in the center of the atom. Thus, Rutherford is credited with the discovery of the atomic nucleus. Despite its numerous breakthroughs, the Rutherford model was neither perfect nor complete. Rutherford proposed that the emission spectrum of hydrogen would look more like a smear rather than being made up of distinct lines. However, this was flawed, as it suggested that atoms can emit energy that isn't quantized. [8]

Niels Bohr, a physicist from Denmark, was able to explain the true nature of electrons by improving on the Rutherford model of the atom. In 1911 Bohr traveled to England in order to study the structure of atoms and molecules. There, he attended lectures on electromagnetism and worked with Rutherford and other scientists such as J. J. Thomson. When he returned to Denmark in 1912, Bohr noticed that in the atomic emissions spectrum of hydrogen, only certain colors could be seen. Thus, he theorized that electrons need to be in energy levels that are quantized. He related the energies of the colors he saw to the differences of hydrogen's energy levels. Although this model is not entirely correct, as it only applies to systems where two charged particles orbit each other, it still has many features that are very applicable to physics today. Later on, scientists such as Werner Heisenberg and Erwin Schrödinger worked to improve upon this model.[9]

Shortcomings of the Bohr Model

Further Reading

Matter and Interactions I Modern Mechanics 4th Edition Chapter 11.10

External links

https://en.wikipedia.org/wiki/Bohr_model

https://en.wikipedia.org/wiki/Quantization_(physics)

https://www.khanacademy.org/science/chemistry/electronic-structure-of-atoms/bohr-model-hydrogen/v/bohr-model-energy-levels

https://www.youtube.com/watch?v=nVW1zDPPZGM

Simulation of Bohr Model:

https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom

Why Bohr's model explains everything around us:

http://scitech.au.dk/en/roemer/apr13/bohrs-model-of-the-atom-explains-science-in-everyday-life/

[1] and image included Simulation by PhET Interactive Simulations, University of Colorado Boulder, licensed under CC-BY-4.0 ( https://phet.colorado.edu ).

[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] Note: All images on this page are either free for commercial use (with no attribution required) or made by myself.

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Bohr Model of the Atom Explained

Planetary Model of the Hydrogen Atom

ThoughtCo / Evan Polenghi

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• Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
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The Bohr Model has an atom consisting of a small, positively charged nucleus orbited by negatively charged electrons. Here's a closer look at this planetary model.

Overview of the Bohr Model

Niels Bohr proposed the Bohr Model of the Atom in 1915. Because the Bohr Model is a modification of the earlier Rutherford Model, some people call Bohr's Model the Rutherford-Bohr Model. The modern model of the atom is based on quantum mechanics. The Bohr Model contains some errors, but it is important because it describes most of the accepted features of atomic theory without all of the high-level math of the modern version. Unlike earlier models, the Bohr Model explains the Rydberg formula for the spectral emission lines of atomic hydrogen .

The Bohr Model is a planetary model in which the negatively charged electrons orbit a small, positively charged nucleus similar to the planets orbiting the sun (except that the orbits are not planar). The gravitational force of the solar system is mathematically akin to the Coulomb (electrical) force between the positively charged nucleus and the negatively charged electrons.

Main Points of the Bohr Model

• Electrons orbit the nucleus in orbits that have a set size and energy.
• The energy of the orbit is related to its size. The lowest energy is found in the smallest orbit.
• Radiation is absorbed or emitted when an electron moves from one orbit to another.

Bohr Model of Hydrogen

The simplest example of the Bohr Model is for the hydrogen atom (Z = 1) or for a hydrogen-like ion (Z > 1), in which a negatively charged electron orbits a small positively charged nucleus. Electromagnetic energy will be absorbed or emitted if an electron moves from one orbit to another. Only certain electron orbits are permitted. The radius of the possible orbits increases as n 2 , where n is the principal quantum number . The 3 → 2 transition produces the first line of the Balmer series . For hydrogen (Z = 1) this produces a photon having wavelength 656 nm (red light).

Bohr Model for Heavier Atoms

Heavier atoms contain more protons in the nucleus than the hydrogen atom. More electrons were required to cancel out the positive charge of all of the protons. Bohr believed each electron orbit could only hold a set number of electrons. Once the level was full, additional electrons would be bumped up to the next level. Thus, the Bohr model for heavier atoms described electron shells. The model explained some of the atomic properties of heavier atoms, which had never been reproduced before. For example, the shell model explained why atoms got smaller moving across a period (row) of the periodic table, even though they had more protons and electrons. It also explained why the noble gases were inert and why atoms on the left side of the periodic table attract electrons, while those on the right side lose them. However, the model assumed electrons in the shells didn't interact with each other and couldn't explain why electrons seemed to stack irregularly.

Problems With the Bohr Model

• It violates the Heisenberg Uncertainty Principle because it considers electrons to have both a known radius and orbit.
• The Bohr Model provides an incorrect value for the ground state orbital angular momentum .
• It makes poor predictions regarding the spectra of larger atoms.
• The Bohr Model does not predict the relative intensities of spectral lines.
• It does not explain fine structure and hyperfine structure in spectral lines.
• The Bohr Model does not explain the Zeeman Effect.

Refinements and Improvements to the Bohr Model

The most prominent refinement to the Bohr model was the Sommerfeld model, which is sometimes called the Bohr-Sommerfeld model. In this model, electrons travel in elliptical orbits around the nucleus rather than in circular orbits. The Sommerfeld model was better at explaining atomic spectral effects, such the Stark effect in spectral line splitting. However, the model couldn't accommodate the magnetic quantum number.

Ultimately, the Bohr model and models based upon it were replaced Wolfgang Pauli's model based on quantum mechanics in 1925. That model was improved to produce the modern model, introduced by Erwin Schrodinger in 1926. Today, the behavior of the hydrogen atom is explained using wave mechanics to describe atomic orbitals.

• Lakhtakia, Akhlesh; Salpeter, Edwin E. (1996). "Models and Modelers of Hydrogen". American Journal of Physics . 65 (9): 933. Bibcode:1997AmJPh..65..933L. doi: 10.1119/1.18691
• Linus Carl Pauling (1970). "Chapter 5-1".  General Chemistry  (3rd ed.). San Francisco: W.H. Freeman & Co. ISBN 0-486-65622-5.
• Niels Bohr (1913). "On the Constitution of Atoms and Molecules, Part I" (PDF). Philosophical Magazine . 26 (151): 1–24. doi: 10.1080/14786441308634955
• Niels Bohr (1914). "The spectra of helium and hydrogen". Nature . 92 (2295): 231–232. doi:10.1038/092231d0
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Model of the Atom (Niels Bohr)

In 1913 one of Rutherford's students, Niels Bohr, proposed a model for the hydrogen atom that was consistent with Rutherford's model and yet also explained the spectrum of the hydrogen atom. The Bohr model was based on the following assumptions.

1. The electron in a hydrogen atom travels around the nucleus in a circular orbit.

2. The energy of the electron in an orbit is proportional to its distance from the nucleus. The further the electron is from the nucleus, the more energy it has.

3. Only a limited number of orbits with certain energies are allowed. In other words, the orbits are quantized.

4. The only orbits that are allowed are those for which the angular momentum of the electron is an integral multiple of Planck's constant divided by 2.

5. Light is absorbed when an electron jumps to a higher energy orbit and emitted when an electron falls into a lower energy orbit.

6. The energy of the light emitted or absorbed is exactly equal to the difference between the energies of the orbits.

Some of the key elements of this hypothesis are illustrated in below. Three points deserve particular attention. First, Bohr recognized that his first assumption violates the principles of classical mechanics. But he knew that it was impossible to explain the spectrum of the hydrogen atom within the limits of classical physics. He was therefore willing to assume that one or more of the principles from classical physics might not be valid on the atomic scale.

Second, he assumed there are only a limited number of orbits in which the electron can reside. He based this assumption on the fact that there are only a limited number of lines in the spectrum of the hydrogen atom and his belief that these lines were the result of light being emitted or absorbed as an electron moved from one orbit to another in the atom.

Finally, Bohr restricted the number of orbits on the hydrogen atom by limiting the allowed values of the angular momentum of the electron. Any object moving along a straight line has a momentum equal to the product of its mass ( m ) times the velocity ( v ) with which it moves. An object moving in a circular orbit has an angular momentum equal to its mass ( m ) times the velocity ( v ) times the radius of the orbit ( r ). Bohr assumed that the angular momentum of the electron can take on only certain values, equal to an integer times Planck's constant divided by 2.

mvr = n h (where n = 1, 2, 3, 4, 5, . . .)

Bohr then used classical physics to show that the energy of an electron in any one of these orbits is inversely proportional to the square of the integer n .  The difference between the energies of any two orbits is therefore given by the following equation.

E = R H 1 - 1

n 1 2 n 2 2

In this equation, n 1 and n 2 are both integers and R H is the proportionality constant known as the Rydberg constant.

Planck's equation states that the energy of a photon is proportional to its frequency.

Substituting the relationship between the frequency, wavelength, and the speed of light into this equation suggests that the energy of a photon is inversely proportional to its wavelength.  The inverse of the wavelength of electromagnetic radiation is therefore directly proportional to the energy of this radiation.  By properly defining the units of the constant, R H , Bohr was able to show that the wavelengths of the light given off or absorbed by a hydrogen atom should be given by the following equation.

1 = R H 1 - 1

Bohr was able to show that the wave-lengths in the UV spectrum of hydrogen discovered by Lyman correspond to transitions from one of the higher energy orbits into the n = 1 orbit. The wavelengths in the visible spectrum of hydrogen analyzed by Balmer are the result of transitions from one of the higher energy orbits into the n = 2 orbit. The Paschen, Brackett, and Pfund series of lines in the infrared spectrum of hydrogen result from electrons dropping into the n = 3, n = 4, and n = 5 orbits, respectively.

The Bohr model did an excellent job of explaining the spectrum of a hydrogen atom.   By incorporating a Z 2 term into the equation, which adjusted for the increase in the attraction between an electron and the nucleus of the atom as the atomic number increased, it could even explain the spectra of ions that contain one electron, such as the He + , Li 2+ , and Be 3+ ions. Nothing could be done, however, to make this model fit the spectra of atoms with more than one electron. The Bohr model left two important questions unanswered. Why are there only a limited number of orbits in which the electron can reside in a hydrogen atom? And, why can't this model be extended to many-electron atoms?

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The Bohr model: The famous but flawed depiction of an atom

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Niels Bohr and quantum theory

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Additional resources:

Bibliography.

The Bohr model, introduced by Danish physicist Niels Bohr in 1913, was a key step on the journey to understand atoms .

Ancient Greek thinkers already believed that matter was composed of tiny basic particles that couldn't be divided further. It took more than 2,000 years for science to advance enough to prove this theory right. The journey to understanding atoms and their inner workings was long and complicated. 

It was British chemist John Dalton who in the early 19th century revived the ideas of ancient Greeks that matter was composed of tiny indivisible particles called atoms. Dalton believed that every chemical element consisted of atoms of distinct properties that could be combined into various compounds, according to Britannica .  

Dalton's theories were correct in many aspects, apart from that basic premise that atoms were the smallest component of matter that couldn't be broken down into anything smaller. About a hundred years after Dalton, physicists started discovering that the atom was, in fact, really quite complex inside. 

Related: There's a giant mystery hiding inside every atom in the universe

The Bohr model: Journey to find structure of atoms

British physicist Joseph John Thomson made the first major breakthrough in the understanding of atoms in 1897 when he discovered that atoms contained tiny negatively charged particles that he called electrons . Thomson thought that electrons floated in a positively charged "soup" inside the atomic sphere, according to Khan Academy .

14 years later, New Zealand-born Ernest Rutherford, Thomson's former student, challenged this depiction of the atom when he found in experiments that the atom must have a small positively charged nucleus sitting at its center. 

Based on this finding, Rutherford then developed a new atom model, the Rutherford model. According to this model, the atom no longer consisted of just electrons floating in a soup but had a tiny central nucleus, which contained most of the atom's mass. Around this nucleus, the electrons revolved similarly to planets orbiting the sun in our solar system , according to Britannica .

Some questions, however, remained unanswered. For example, how was it possible that the electrons didn't collapse onto the nucleus, since their opposite charge would mean they should be attracted to it? Several physicists tried to answer this question including Rutherford's student Niels Bohr.

Bohr was the first physicist to look to the then-emerging   quantum theory to try to explain the behavior of the particles inside the simplest of all atoms; the atom of hydrogen. Hydrogen atoms consist of a heavy nucleus with one positively-charged proton around which a single, much smaller and lighter, negatively charged electron orbits. The whole system looks a little bit like the sun with only one planet orbiting it. 

Bohr tried to explain the connection between the distance of the electron from the nucleus, the electron's energy and the light absorbed by the hydrogen atom, using one great novelty of physics of that era: the Planck constant. 

The Planck constant was a result of the investigation of German physicist Max Planck into the properties of electromagnetic radiation of a hypothetical perfect object called the black body. 

Strangely, Planck discovered that this radiation, including light, is emitted not in a continuum but rather in discrete packets of energy that can only be multiples of a certain fixed value, according to Physics World .That fixed value became the Planck constant. Max Planck called these packets of energy quanta, providing a name to the completely new type of physics that was set to turn the scientists' understanding of our world upside down.

The Bohr model and the hydrogen atom

What role does the Planck constant play in the hydrogen atom? Despite the nice comparison, the hydrogen atom is not exactly like the solar system. The electron doesn't orbit its sun —the nucleus — at a fixed distance, but can skip between different orbits based on how much energy it carries, Bohr postulated. It may orbit at the distance of Mercury , then jump to Earth , then to Mars . 

The electron doesn't slide between the orbits gradually, but makes discrete jumps when it reaches the correct energy level, quite in line with Planck's theory, physicist Ali Hayek explains on his YouTube channel .

Bohr believed that there was a fixed number of orbits that the electron could travel in. When the electron absorbs energy, it jumps to a higher orbital shell. When it loses energy by radiating it out, it drops to a lower orbit. If the electron reaches the highest orbital shell and continues absorbing energy, it will fly out of the atom altogether.

The ratio between the energy of the electron and the frequency of the radiation it emits is equal to the Planck constant. The energy of the light emitted or absorbed is exactly equal to the difference between the energies of the orbits and is inversely proportional to the wavelength of the light absorbed by the electron, according to Ali Hayek.

Using his model, Bohr was able to calculate the spectral lines — the lines in the continuous spectrum of light — that the hydrogen atoms would absorb. 

The shortcomings of the Bohr model

The Bohr model seemed to work pretty well for atoms with only one electron. But apart from hydrogen, all other atoms in the periodic table have more, some many more, electrons orbiting their nuclei. For example, the oxygen atom has eight electrons, the atom of iron has 26 electrons.

Once Bohr tried to use his model to predict the spectral lines of more complex atoms, the results became progressively skewed.

There are two reasons why Bohr's model doesn't work for atoms with more than one electron, according to the Chemistry Channel . First, the interaction of multiple atoms makes their energy structure more difficult to predict. 

Bohr's model also didn't take into account some of the key quantum physics principles, most importantly the odd and mind-boggling fact that particles are also waves, according to the educational website Khan Academy .

As a result of quantum mechanics, the motion of the electrons around the nucleus cannot be exactly predicted. It is impossible to pinpoint the velocity and position of an electron at any point in time. The shells in which these electrons orbit are therefore not simple lines but rather diffuse, less defined clouds. 

 — Massive Space Structures Have Surprising Connection to Quantum Mechanics Math —   Why Can't Quantum Mechanics Explain Gravity? (Op-Ed) — Do We Live in a Quantum World?  

Only a few years after the model's publication, physicists started improving Bohr's work based on the newly discovered principles of particle behavior. Eventually, the much more complicated quantum mechanical model emerged, superseding the Bohr model. But because things get far  less neat when all the quantum principles are in place, the Bohr model is probably still the first thing most physics students discover in their quest to understand what governs matter in the microworld. 

Read more about the Bohr atom model on the website of the National Science Teaching Association or watch this video .

Heilbron, J.L., Rutherford–Bohr atom, American Journal of Physics 49, 1981 https://aapt.scitation.org/doi/abs/10.1119/1.12521

Olszewski, Stanisław, The Bohr Model of the Hydrogen Atom Revisited, Reviews in Theoretical Science, Volume 4, Number 4, December 2016 https://www.ingentaconnect.com/contentone/asp/rits/2016/00000004/00000004/art00003

Kraghm Helge, Niels Bohr between physics and chemistry, Physics Today, 2013 http://materias.df.uba.ar/f4Aa2013c2/files/2012/08/bohr2.pdf

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Niels Bohr summary

Niels Bohr , (born Oct. 7, 1885, Copenhagen, Den.—died Nov. 18, 1962, Copenhagen), Danish physicist. He studied the structure of the atom with J.J. Thomson and Ernest Rutherford at the universities of Cambridge and Manchester. He was among the first to see the importance of an element’s atomic number and postulated that any atom could exist only in a discrete set of states characterized by definite values of energy. He became the first to apply the quantum theory to atomic and molecular structure, and his concept of the atomic nucleus was a key step in understanding such processes as nuclear fission . From 1920 to 1962 he directed the newly created Institute for Theoretical Physics in Copenhagen. His work on atomic theory won him a Nobel Prize for Physics in 1922. He was president of the Royal Danish Academy from 1939 until his death. Though he contributed to atomic bomb research in the U.S. during World War II, he later dedicated himself to the cause of arms control. He received the first U.S. Atoms for Peace Award in 1957. Element 107, bohrium, is named in his honour. His son Aage Niels Bohr shared the 1975 Nobel Prize for Physics with Ben Mottelson and James Rainwater for their work on atomic nuclei.

Niels Bohr Atomic Model Theory Experiment

Niels Bohr Education & Life

Niels Bohr is a well-known Danish physicist that spent the majority of his life studying the atomic model. The atomic model is a theory that holds that the atoms in an element are different from one another and contain protons, electrons, and neutrons.

What Was Niels Bohr Experiment? What Did Niels Bohr Discover?

The Niels Bohr Atomic Model theory is a model that was introduced by Niels Bohr in 1913 to describe the atom. It was a postulation of Bohr that the electrons rotated in a circular orbit around the nucleus of the atom.

Niels Bohr’s atomic model was created based on previous research by Rutherford, Rutherford’s gold foil experiment, and Ernest Rutherford’s model of the atom.

In his model, Bohr postulated that electrons were placed in orbits that are referred to as orbitals. Atoms consist of a central nucleus, surrounded by electrons in orbital shells.

The electrons sit in energy levels around the nucleus, with the lowest possible energy level being electron number one and the highest being electron number eight.

The Bohr atomic model theory states that atoms are composed of a nucleus, which consists of one or more protons and neutrons that are held together by nuclear forces.

It is also known as a hydrogen atom model or the Rutherford-Bohr Atomic Model Theory.

Niels Bohr was a Danish physicist who had a theory about atoms that he called the “atomic model”. Bohr’s atomic model had a nucleus with a certain number of positively charged particles that were held together by negatively charged particles. The electrons would orbit around the nucleus of the atom.

Atomic Model Theory is the idea that the electrons orbiting the atom don’t orbit around a stationary nucleus like they were on the earth in a solar system. Instead, the electrons orbit around the nucleus of the atom, which is constantly moving.

This is what Bohr called his quantum leap. Bohr’s theory helped to explain the interference experiment and helped to create quantum theories, like the wave-particle duality

Niels Bohr came up with a model of the atom that was entirely radical for its time. It contradicted much of what was previously believed about atoms and electrons.

He believed that an electron orbits a nucleus, which is made up of a group of subatomic particles. Bohr received the Nobel Prize in 1922 for his theory.

Niels Bohr As A Physicist

Niels Bohr is considered to be one of the greatest physicists in history. He worked for many years on physics, teaching, and management. This work led him to become a professor at the University of Copenhagen for thirty years.

In 1912, he was offered a professorship at the Institute of Theoretical Physics in Stockholm. However, there was a problem with his salary because he was not on an equal footing with his counterpart at Uppsala University.

In 1920, Bohr returned to the Institute of Theoretical Physics in Copenhagen. To this day, Bohr remains one of the most celebrated people in Danish history.

Niels Bohr as a Father and a Husband

In 1908, Niels Bohr married Margrethe Nørlund. They had two sons, Aage Nørlund (1909) and Harald Bohr (1911). In 1920, they moved to King’s Gate No.1.

They remained there for the rest of their lives. Bohr was a caring husband and father, who did not like to leave home too often because he missed his family.

Bohr also liked to play classical music, and he was a good enough pianist to give concerts in Copenhagen.

Niels Bohr’s Death

In 1942, Niels Bohr became increasingly ill and was diagnosed with an incurable muscle disease, which caused him great pain and robbed him of his ability to walk.

In September 1948, Bohr became very ill. He developed a blood clot in his leg and he could no longer move around on his own. On October 17, he suffered a severe stroke. He passed away on 18 November.

After his death, the Danish king said about Bohr: “I know of no one who has contributed more to the knowledge and to the progress of mankind than Niels Bohr”.

Niels Bohr’s Legacy

One of the most important things that Niels Bohr did was to create a new model of the atom. He realized that electrons could exist in ‘allowed’ orbits, but they could also ‘jump’, or transition, to higher energy orbits.

One way that people continued to think about Bohr’s ideas was through the use of his concept of quantum jumps.

Bohr also believed that the electron didn’t exist in any particular orbit, but instead was found in all orbits all at the same time, and that only when we looked at an atom would it ‘decide’ which orbit to be in.

He was awarded the Nobel Prize for physics in 1922 for this work.

The Bohr Model of The Atom

Bohr’s model of the atom was one of the most important contributions of his career because it helped us to understand why atoms didn’t collapse.

However, Bohr’s model didn’t explain all the properties of an atom. For example, in the ‘old model of the atom, electrons were stationary (always in the same orbit), and they were at a fixed distance from their nucleus. In other words, they orbited at a fixed distance from their nucleus.

Now, with Bohr’s model, this wasn’t true anymore – electrons could jump around to different orbits. It’s easy to understand that if electrons can jump around, then they can’t have a fixed distance from the nucleus. They would also have to be influenced by the nucleus.

So, when you measure any of the properties of an atom (e.g. the position of an electron), you can never measure it as if it were in ‘absolute space’, but only as how things are relative to each other (relative motion).

What Is Niels Bohr Known For?

The physics community remembers Niels Bohr for his work with the Bohr model of the atom. He was able to explain and interpret vast amounts of experimental data in terms of his atomic model.

The Bohr atomic model consists of one positively charged nucleus surrounded by electrons, which are negatively charged.

The positive charge in the nucleus is balanced by negative charge in the electron. Bohr argued that electrons move around the atom by radially oscillating, which wiggles their position in space.

Bohr also thought that atoms could be described as a series of stationary orbitals. An orbital can be considered a “shell” around an electron and “is filled” with electrons.

Energy can be transferred between an orbital and the electron by oscillations. Bohr provided the mathematical description of his model by applying quantum mechanics.

For example, the electron orbits are given by Schrödinger wave equations. The radius of the orbits is related to energy levels in a very simple way.

These are the most basic atomic model equations ever published. All other models have been derived from these basic ones.

Bohr himself made sure that the model could be applied to spectroscopy and other measurements.

What Is Niels Bohr Famous For?

Niels Bohr was a physicist who made fundamental contributions to the theory of the atom, quantum mechanics, and chemical bonding.

He is also known as the father of modern quantum physics. Bohr was one of the first to apply mathematics to physics. He was able to think in terms of waves and positions instead of just particles and points.

Niels Bohr’s Influence On Chemistry

Bohr’s influence also extended beyond physics. In fact, he made some interesting contributions to chemistry.

For example, he correctly predicted that helium atoms would absorb high-frequency light in a series of elements (helium, neon, argon, and krypton).

He also predicted that they would emit light in a series of elements (for example sodium). But perhaps his most important contribution to chemistry was helping to explain why certain chemical reactions occur.

Bohr’s ideas about quantum jumps also helped us to understand how hydrogen, which has a very large atomic mass, could be broken up into its component atoms.

He explained that a hydrogen atom consists of only one electron which moves around the nucleus. The electron orbits the nucleus and then jumps to a new energy level.

Another of Bohr’s greatest contributions was his work in spectroscopy. He correctly predicted that the frequency of light would increase when light passed through a series of metals (such as helium and sodium).

He also predicted that these elements would emit photons at visible frequencies when heated.

The Bohr Model And Quantum Mechanics

While the basic idea behind Bohr’s model (the atom is made up of electrons that move around a nucleus) is still in use today, it was eventually superseded by quantum mechanics .

However, Bohr’s ideas were very important for understanding how atoms worked. He showed how the strangeness of quantum physics explained why atoms didn’t collapse.

He also showed how the strangeness of quantum physics could be used to explain how atoms absorb and emit light.

While Bohr’s model did not explain some of the properties of atoms (mass, charge, or size), it had a major influence on the way that we think about and study atoms today.

Niels Bohr And Experimental Data

Bohr was a physicist who was very important to experimentalists. His contributions helped to explain how electrons could jump from one orbit to another in an atom.

It also helped explain why different atoms have different masses and predicted light emission colors for various kinds of spectroscopy.

In addition, Bohr was one of the first to suggest that the cathode rays (later to be called electrons) do not actually have a definite trajectory but instead travel in a broad wave with peaks and troughs. The wave theory described the behavior of electrons much better than the Newtonian particle model, which had been used up until then.

What Did Niels Bohr Think About The Atom And Quantum Mechanics?

According to Bohr, an atom is composed of a charged nucleus and a cloud of electrons. The nucleus is fixed in space, while the electrons can move around inside the atom.

This movement happens very quickly but is maintained by electromagnetic forces. It is also maintained by the energy which keeps the electrons in their orbits. Ionization occurs when an electron jumps from one orbit to another – or when light from a specific wavelength enters an atom.

Bohr was very conscious of the fact that he was a ‘complementary’ physicist. This means that he accepted quantum theory, but also believed in the classical view (which has all particles having definite locations).

In his day, this challenged the idea of quantum mechanics, since it meant that Bohr himself did not believe in quantum theory.

This is because Bohr did not equate the accuracy of his predictions with the validity of theoretical physics.

However, since he never really discussed these views with his colleagues, and because the laws of quantum mechanics were absolutely consistent with all of his predictions, Bohr did not suffer any significant criticism.

What Was Niels Bohr’s Contribution To Quantum Mechanics?

In 1913 Bohr began working on what we now call the “old” model of an atom. Before this time, it was thought that electrons orbited the nucleus in evenly spaced orbits.

It was also thought that electrons jumped to a new orbit when they gained or lost energy. Bohr changed this view completely by introducing the idea of stationary, allowed orbits.

This meant that electrons had a certain angular momentum inside the atom, which was ever-changing.

An electron could jump to another orbit by losing or gaining energy but did not jump because of an external push or pull. In other words, electrons jump because they are excited by the electromagnetic radiation of an atom.

The idea of stationary allowed orbits was revolutionary. It meant that atoms could emit and absorb energy in a continuous way, rather than in individual packets (which is what happened when people used the Bohr-Ellsberg-Slater theory).

In 1914, Bohr suggested that electrons could exist only in certain orbits inside the atom. This meant that there was a mathematical connection between atomic orbitals and wavelengths or frequencies of light.

Later, in 1916, Bohr suggested that the atom is mainly made of neutrons. He also introduced the idea of electron jumping. This was significant because it was one of the first models to combine quantum theory and classical physics.

In 1918 Bohr published an explanation for atomic structure based on a “postulate” about what happened when electrons jumped from one orbit to another.

According to Bohr, electrons could exist only in certain orbits (i.e., certain energy levels). Electrons could also jump from one orbit into another.

This was an important development in quantum mechanics because it helped to explain why the atom would not collapse.

What Did Niels Bohr Contribute To Society?

Bohr was one of the founders of quantum mechanics. This theory is still in use today. In addition, Bohr was one of the first people to think about atoms – what they might be like and how we can observe them.

He developed models which are still used today.

Besides this, Bohr was a very successful teacher and mentor. Many young scientists (including future Nobel Prize winners) studied with him in Copenhagen and benefited from his advice and guidance.

Niels Bohr was one of the first people to suggest that the laws of classical physics could be thought of as being the same as the laws of quantum physics.

This was a revolutionary idea, and it showed that everything in our world is quantifiable. In other words, nothing in our world can escape quantification – or measurement.

This view of reality – or what we would call ‘the scientific method’ – has had a huge influence on modern thinking about how our society works.

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