Bohr's Quantization of Angular Momentum

In summary: The electron is like a tiny standing wave with a certain frequency. Bohr's second postulate says that it is only possible for an electron to move in an orbit for which its orbital angular momentum L is an integral multiple of \hbar.
  • #1
msavg
3
0
Bohr's second postulate says that it is only possible for an electron to move in an orbit for which its orbital angular momentum L is an integral multiple of [tex]\hbar[/tex].

Can somebody please derive and explain L= n[tex]\hbar[/tex] for me?

I feel like a total dummy for not understanding this, but this is what I have so far:

L= mrv

L=pr, p= hf/c, f= w/2pi, where w is the angular frequency and w= v/r

L= [tex]\hbar[/tex]wr/c = [tex]\hbar[/tex]v/c ??

Yeah... I'm obviously missing something...
:\

Help?(Thank you in advance.)
 
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  • #2
Welcome to physicsforums msavg,

the argument goes like this:
You interpret the electron as a standing wave as depicted http://www.personal.psu.edu/faculty/g/x/gxm21/A/Mayer-RingofFire_files/image003L.jpg [Broken]. A circle has circumference [tex]C=2 \pi r[/tex] and the condition for a standing wave is [tex]C=n \lambda[/tex]. From these two equations we get [tex]n \lambda = 2 \pi r[/tex].

De Broglie says [tex]\lambda = h / p[/tex]. Can you proceed?

(Edit: I changed the letter for circumference from L to C since it collides with the notation for the angular momentum)
 
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  • #3
Edgardo said:
Welcome to physicsforums msavg,

the argument goes like this:
You interpret the electron as a standing wave as depicted http://www.personal.psu.edu/faculty/g/x/gxm21/A/Mayer-RingofFire_files/image003L.jpg [Broken]. A circle has circumference [tex]C=2 \pi r[/tex] and the condition for a standing wave is [tex]C=n \lambda[/tex]. From these two equations we get [tex]n \lambda = 2 \pi r[/tex].

De Broglie says [tex]\lambda = h / p[/tex]. Can you proceed?

(Edit: I changed the letter for circumference from L to C since it collides with the notation for the angular momentum)


Thank you.
:)

I knew I was missing something. This makes a whole lot more sense in context of standing waves.
 
Last edited by a moderator:

1. What is Bohr's Quantization of Angular Momentum?

Bohr's Quantization of Angular Momentum is a fundamental principle in quantum mechanics that states that the angular momentum of an electron in an atom is quantized, meaning it can only have certain discrete values.

2. How does Bohr's Quantization of Angular Momentum relate to the Bohr model of the atom?

The Bohr model of the atom was based on Bohr's Quantization of Angular Momentum, as it proposed that electrons move around the nucleus in specific orbits with fixed angular momentum values.

3. What is the significance of Bohr's Quantization of Angular Momentum?

Bohr's Quantization of Angular Momentum was a major breakthrough in understanding the behavior of electrons in atoms. It helped explain the stability of atoms and laid the foundation for further developments in quantum mechanics.

4. How does Bohr's Quantization of Angular Momentum differ from classical mechanics?

In classical mechanics, angular momentum can have any continuous value, while in Bohr's Quantization of Angular Momentum, it is restricted to discrete values. This is because electrons in atoms behave like waves rather than particles, as explained by quantum mechanics.

5. Can Bohr's Quantization of Angular Momentum be applied to other systems besides atoms?

Yes, Bohr's Quantization of Angular Momentum can be applied to any system in which a particle moves in a circular or elliptical orbit around a central point, such as planetary motion or the motion of charged particles in a magnetic field.

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