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  • Show mathematically how Bohr's postulate of quantization of orbital angular momentum in hydrogen atom is explained by de-Broglie's hypothesis.     <div style="float:left; wid

Show mathematically how Bohr's postulate of quantization of orbital angular momentum in hydrogen atom is explained by de-Broglie's hypothesis.

 

 
 
 
 
 

Answers (1)

The de Broglie's wavelength

\lambda =\frac{h}{mV}\; \; ---(1)

For stationary orbit

2\pi r=n\lambda \; \; \; \; \; \; ---(2)

Substituting the value of \lambda from (1) and (2)

2\pi r=\frac{nh}{mV}

mVr=\frac{nh}{2\pi }

mVr=L (Orbital angular momentum)

L=\frac{nh}{2\pi }

That is orbital angular momentum is an integral multiple of \frac{h}{2\pi } (Bohr's postulate of quantization of orbital angular momentum)

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