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
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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1 Answer
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According to Bohr’s theory,
mvr = nh / 2π
=> 2πr = nh/mv
=> mv = nh / 2πr - (i)
According to de Broglie equation,
h / λ - (ii)
Comparing equations (i) and (ii)nh / 2πr = h / λ
=> 2πr = n λ
Thus, the circumference (2πr) of the Bohr orbit for hydrogen atom is an integral multiple of the de Broglie wavelength.
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