Linus Pauling's Hydrogen Atom: MVR=nh/2pi?

In summary, Linus Pauling's Hydrogen Atom equation is a mathematical representation of the relationship between the mass, velocity, and energy of an electron in a hydrogen atom. It was derived from classical and quantum mechanics principles and has had significant impacts on our understanding of atomic structure and quantum mechanics. It is still relevant today in the field of quantum mechanics and is used in modern research.
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The_ArtofScience
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I was reading Linus Pauling's "General Chemistry" when I noticed something that didn't quite fit. The angular momentum for the hydrogen atom was described as equivalent to n times h/2pi. Does anyone know why this statement is true? I've tried googling it and still can't seem to figure out how mvr= nh/2pi. The problematic part is the "n," how could you possiby denote a quantum number as anything but position?
 
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Nevermind, I found out how to get it!
 
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I can provide some insight into this question. The statement MVR=nh/2pi is known as the Bohr-Sommerfeld quantization condition for the hydrogen atom. It was first proposed by Niels Bohr in 1913 and later refined by Arnold Sommerfeld in 1916. This formula describes the allowed energy levels for the electron in a hydrogen atom, where M is the angular momentum, V is the velocity, R is the radius of the orbit, n is the principal quantum number, and h is Planck's constant.

The key concept here is that in the quantum world, particles such as electrons can only exist in certain discrete energy levels, or orbits, around the nucleus. These energy levels are determined by the principal quantum number, n. This number represents the different possible states that an electron can occupy, and it is related to the energy and angular momentum of the electron.

The equation MVR=nh/2pi is a mathematical representation of this concept. It shows that the angular momentum of the electron (MVR) is quantized, meaning it can only take on certain values determined by the principal quantum number (n). This is similar to how the energy of the electron is quantized, as described by the equation E=nhv, where v is the frequency of the electron's orbit.

In summary, the statement MVR=nh/2pi is true because it is a fundamental principle of quantum mechanics that describes the allowed energy levels for the electron in a hydrogen atom. The "n" in the equation represents the principal quantum number, which is a fundamental property of particles in the quantum world.
 

1. What is Linus Pauling's Hydrogen Atom equation?

Linus Pauling's Hydrogen Atom equation is MVR=nh/2pi, where M is the mass of the electron, V is the velocity of the electron, R is the radius of the electron's orbit, n is the principal quantum number, and h is Planck's constant divided by 2 pi.

2. What does the MVR=nh/2pi equation represent?

This equation represents the relationship between the mass, velocity, and energy of an electron in a hydrogen atom. It is also known as the Bohr-Sommerfeld equation, which was proposed by Niels Bohr and refined by Arnold Sommerfeld and Linus Pauling.

3. How is the MVR=nh/2pi equation derived?

The MVR=nh/2pi equation is derived from the principles of classical mechanics and quantum mechanics. It combines the classical equations for the motion of a charged particle in a circular orbit with the quantum mechanical concept of quantized energy levels in an atom.

4. What is the significance of the MVR=nh/2pi equation?

The MVR=nh/2pi equation is significant because it provides a mathematical description of the energy levels and orbits of electrons in a hydrogen atom. This equation was a major breakthrough in understanding the structure of atoms and laid the foundation for the development of quantum mechanics.

5. Is the MVR=nh/2pi equation still relevant today?

Yes, the MVR=nh/2pi equation is still relevant today in the field of quantum mechanics. While it was originally developed for the hydrogen atom, it has been applied to other atoms and molecules as well. It is also used in modern research to study the behavior of electrons in different materials and environments.

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