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(A) The number of waves produced by an electron in one complete revolution is given by the ratio of the circumference of the orbit to the de Broglie w

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$n$

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(A) The number of waves produced by an electron in one complete revolution is given by the ratio of the circumference of the orbit to the de Broglie wavelength of the electron.Number of waves $= \frac{	ext{Circumference}}{\lambda} = \frac{2 \pi r}{\lambda}$According to de Broglie's hypothesis,$\lambda = \frac{h}{mv}$.Substituting this into the expression,we get: Number of waves $= \frac{2 \pi r}{(h / mv)} = \frac{2 \pi mvr}{h}$.According to Bohr's postulate,the angular momentum $mvr = \frac{nh}{2 \pi}$.Therefore,substituting $mvr$ into the expression: Number of waves $= \frac{2 \pi}{h} 	imes \frac{nh}{2 \pi} = n$.Thus,the number of waves is equal to the principal quantum number $n$.

Number of waves produced by an electron in one complete revolution in $n^{th}$ orbit is

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