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Column I Column II
A Frequency of orbiting electron P is directly proportional to $Z^{2}$
B Angular momentum of orbiting electron Q is directly proportional to n
C Magnetic moment of orbiting electron R is inversely proportional to $n^{3}$
D The average current due to orbiting of electron S is independent of Z

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$A - P R, B - Q S, C - P R, D - P Q$

$A - P R, B - P S, C - P Q, D - Q R$

$A - P R, B - Q S, C - Q S, D - P R$

$A - P S, B - Q S, C - P R, D - P Q$

answer is B.

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Detailed Solution

$f = \frac{m Z_{}^{2} e^{4}}{4 \in_{0}^{2} h^{3} n^{3}} \Rightarrow f α \frac{z^{2}}{n^{3}} \Rightarrow L = \frac{n h}{2 π} \Rightarrow L α n \begin{array}{l} M = \frac{e}{2 m} L = \frac{e}{2 m} (\frac{n h}{2 π}) \\ M α n \\ I = \frac{e v}{2 π r} = \frac{e}{2 π} [\frac{π m Z e^{2}}{n^{2} h^{2} \in_{0}}] [\frac{Z e^{2}}{2 \in_{0} n h}] \Rightarrow I α \frac{z^{2}}{n^{3}} \end{array}$

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