Chemistry - Atomic Structure Question with Solution | TestHub

Question Explanation: Find the ratio of time.

Concept : This question is based on Bohr Model

Solution:

$$\mathrm{r}=0.529\frac{{\mathrm{n}}^2}{\mathrm{z}}{\mathrm{A}}^{\circ }$$

$\frac{r_1}{r_2}={\left(\frac{n_1}{n_2}\right)}^2=\frac{R}{4R}$

$\frac{{\mathrm{n}}_1}{{\mathrm{n}}_2}=\frac{1}{2}$

Time period of Revolution $=\frac{2\pi r}{v}$

$r\propto \frac{n^2}{z};v\propto \frac{z}{n}$

$\mathrm{T}\propto \frac{{\mathrm{n}}^3}{{\mathrm{z}}^2}$

$\mathrm{z}=1$

$\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}={\left(\frac{{\mathrm{n}}_1}{{\mathrm{n}}_2}\right)}^3={\left(\frac{1}{2}\right)}^3=\frac{1}{8}$

Final Answer: option (c)