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  • Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

2.32    Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

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According to the Bohr's postulate of angular momentum,

mvr=\frac{nh}{2\pi} 

which can be written as:   2\pi r=\frac{nh}{mv}.....................................(1)

Then according to de Broglie's equation for wavelength, 

\lambda = \frac{h}{mv}                                                                     ......................................(2)

Now, substituting the values of equation (2) in equation (1) we get,

2\pi r = n\lambda

Thus, the circumference of the Bohr's orbit for the hydrogen atom is an integral multiple of de Broglie's wavelength associated with the electron revolving around the orbit.

Posted by

Divya Prakash Singh

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