According to Bohr’s atomic theory :-
Question:

According to Bohr’s atomic theory :-

(A) Kinetic energy of electron is $\propto \frac{Z^{2}}{n^{2}}$.

(B) The product of velocity (v) of electron and principal quantum number $(\mathrm{n})$, ‘vn’ $\propto Z^{2}$

(C) Frequency of revolution of electron in an

orbit is $\propto \frac{Z^{3}}{n^{3}}$.

(D) Coulombic force of attraction on the

electron is $\propto \frac{Z^{3}}{n^{4}}$.

Choose the most appropriate answer from the options given below :

1. (C) Only

2. (A) Only

3. (A), (C) and (D) only

4. (A) and (D) only

Correct Option: 4,

Solution:

According to Bohr’s theory :

(A) $\mathrm{KE}=13.6 \frac{\mathrm{z}^{2}}{\mathrm{n}^{2}} \frac{\mathrm{eV}}{\text { atom }} \Rightarrow \mathrm{KE} \alpha \frac{\mathrm{z}^{2}}{\mathrm{n}^{2}}$

(B) speed of $\mathrm{e}^{-} \alpha \frac{\mathrm{z}}{\mathrm{n}}$

(C) Frequency of revolution of $\mathrm{e}^{-}=\frac{\mathrm{v}}{2 \pi \mathrm{r}}$

(D) $\mathrm{F}=\frac{\mathrm{kq}_{1} \mathrm{q}_{2}}{\mathrm{r}^{2}}=\frac{\mathrm{kze}^{2}}{\mathrm{r}^{2}} \quad\left\{\mathrm{r} \alpha \frac{\mathrm{n}^{2}}{\mathrm{z}}\right.$

$\Rightarrow \mathrm{F} \alpha \frac{\mathrm{z}}{\left(\frac{\mathrm{n}^{2}}{\mathrm{z}}\right)^{2}}$