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Quantum Physics Derivation

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In the guide for Physics HL, it says that one of the understandings in Quantum physics is

'Quantization of angular momentum in the Bohr model for hydrogen' 

But the quantization of angular momentum comes up in a really long and kind of confusing derivation for the formula rn=n2h2/4(pi)2ke2m.

The formula isn't given in the data booklet, so do we need to know it and its derivation? Or do we just have to qualitatively understand Bohr's model?

Edited by pdgcm

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Quantization of angular momentum is indeed used in deriving the formula you quoted; however, it is very fundamental to quantum mechanics and isn't just buried in that derivation.  Bohr assumed (quite extraordinarily) that the angular momentum of an electron orbiting a proton could only have certain (quantized) values of angular momentum (L = mvr).  He assumed that the angular momentum was an integer multiple of some basic unit h/(2pi) where h is Planck's constant.  Because of this quantization condition you get the result that the electron only exists at certain radii given by the formula you quoted.  

His condition for quantization of angular momentum can be stated as:   mvr = n [h/(2pi)]  where n can only be an integer.  So angular momentum can't take on any value between n=1 and n=2, only exactly n=1 and n=2.

That equation is, in fact, in the IB data booklet, so I would say you need to be familiar with this both qualitatively and quantitatively.

It also leads to another equation that is in the data booklet E = -13.6/n2, which shows how the energy levels of a hydrogen atom vary with n. 

Source:  I'm an IB physics teacher, and Tsokos has a great write-up of this in the 6th edition of Physics for the IB Diploma on page 492.

 

Edited by bsimps3
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13 hours ago, bsimps3 said:

Quantization of angular momentum is indeed used in deriving the formula you quoted; however, it is very fundamental to quantum mechanics and isn't just buried in that derivation.  Bohr assumed (quite extraordinarily) that the angular momentum of an electron orbiting a proton could only have certain (quantized) values of angular momentum (L = mvr).  He assumed that the angular momentum was an integer multiple of some basic unit h/(2pi) where h is Planck's constant.  Because of this quantization condition you get the result that the electron only exists at certain radii given by the formula you quoted.  

His condition for quantization of angular momentum can be stated as:   mvr = n [h/(2pi)]  where n can only be an integer.  So angular momentum can't take on any value between n=1 and n=2, only exactly n=1 and n=2.

That equation is, in fact, in the IB data booklet, so I would say you need to be familiar with this both qualitatively and quantitatively.

It also leads to another equation that is in the data booklet E = -13.6/n2, which shows how the energy levels of a hydrogen atom vary with n. 

Source:  I'm an IB physics teacher, and Tsokos has a great write-up of this in the 6th edition of Physics for the IB Diploma on page 492.

 

I must have missed that formula in the data booklet. Thanks a lot! You really cleared that up for me.

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