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Question 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.

Answer

The angular momentum of an electron = mvr = nh/2π --------------1

Also according to de Broglie equation λ = h/mv

Or

mv = h/v -----------2

Putting 2 in 1

h/v =nh/2π or 2λr= nλ

Since ‘2πr’ represents the circumference of the Bohr orbit (r), it is proved by equation (3) that the circumference of the Bohr orbit of the hydrogen atom is an integral multiple of de Broglie’s wavelength associated with the electron revolving around the orbit.

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