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(B) According to Bohr's model for a hydrogen atom:$1$. Angular momentum $L = \frac{nh}{2\pi}$,so $L \propto n$.$2$. Orbit radius $r = a_0 \frac{n^2}{Z

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$frL$ is constant for all orbits

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(B) According to Bohr's model for a hydrogen atom:$1$. Angular momentum $L = \frac{nh}{2\pi}$,so $L \propto n$.$2$. Orbit radius $r = a_0 \frac{n^2}{Z}$,so $r \propto n^2$ (for a fixed $Z$).$3$. Frequency of revolution $f = \frac{v}{2\pi r}$. Since $v \propto \frac{Z}{n}$ and $r \propto \frac{n^2}{Z}$,we have $f \propto \frac{Z/n}{n^2/Z} = \frac{Z^2}{n^3}$,so $f \propto n^{-3}$.Now,consider the product $frL$:$frL \propto (n^{-3}) \cdot (n^2) \cdot (n) = n^0 = 1$.Therefore,$frL$ is independent of the quantum number $n$ and is constant for all orbits.

The magnitude of angular momentum,orbit radius,and frequency of revolution of an electron in a hydrogen atom corresponding to quantum number $n$ are $L, r$,and $f$ respectively. According to Bohr's theory of the hydrogen atom,which of the following is constant for all orbits?

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