Question

In each situation of List 1, a physical quantity related to orbiting electron in hydrogen-like atom is given. The terms $"Z"$ and $‘n^{\prime }$ given in list 2 have usual meaning in Bohr's theory. Match the quantities in List 1 with the terms in list 2

Answer 1

A) frequency of revolving electron = $\frac{z^2}{n^3}$

hence, Frequency of orbiting electron Is directly proportional to $z^2$ and inversely proportional to $n^3$ .

B) Angular momentum of orbiting electron = $\frac{nh}{2\pi }$

hence , Angular momentum of orbiting electron , Is directly proportional to n and Is independent of Z .

C) ${\mu }_z={\mu }_B\sqrt{l(l+1)}.$

as l depends upon n .

Hence , Magnetic moment of orbiting electron Is directly proportional to n and Is independent of Z .

D) $i_{avg}=\frac{q}{t}=\frac{e}{\frac{2\pi }{\omega }}=\frac{e\omega }{2\pi }$

$\omega =\frac{v_n}{r_n}$

As we know ,

$v_n$ is directly proportional to $\frac{z}{n}$

$r_n$ is directly proportional to $\frac{n^2}{z}$

Putting , the values and simplying , we get :

$i_{avg}$ is directly proportional to $\frac{z^2}{n^3}$.

Hence , The average current due to orbiting of electron Is directly proportional to $z^2$ and inversely proportional to $n^3$ .