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(A) According to the Bohr model,the radius of the $n^{th}$ orbit is given by $r_n = \frac{n^2 h^2}{4 \pi^2 m k Z e^2}$.For a hydrogen atom,$Z = 1$,so

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$p_n \propto \frac{1}{n}$

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(A) According to the Bohr model,the radius of the $n^{th}$ orbit is given by $r_n = \frac{n^2 h^2}{4 \pi^2 m k Z e^2}$.For a hydrogen atom,$Z = 1$,so $r_n \propto n^2$.The velocity of an electron in the $n^{th}$ orbit is given by $v_n = \frac{2 \pi k Z e^2}{nh}$.Since $Z = 1$,$v_n \propto \frac{1}{n}$.The linear momentum $p_n$ is defined as $p_n = m v_n$.Since $m$ is constant,$p_n \propto v_n$.Therefore,$p_n \propto \frac{1}{n}$.

In the Bohr model of the hydrogen atom,the linear momentum of the electron depends on the principal quantum number $n$ as:

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