Q142 / 200 · NEET 2022 (Phase 2) · Physics

Let $R_1$ be the radius of the second stationary orbit and $R_2$ be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio $\frac{R_1}{R_2}$ is:

  • Correct answer
    A
    0.25
  • B
    0.5
  • C
    2
  • D
    4

Solution

As, $\begin{aligned} \mathrm{R}_n & =0.529 \frac{n^2}{\mathrm{Z}} \\ \text { Hence, } \quad \frac{\mathrm{R}_1}{\mathrm{R}_2} & =\frac{0.529 \frac{n_1^2}{\mathrm{Z}_1}}{0.529 \frac{n_2^2}{\mathrm{Z}_2}} \\ \frac{\mathrm{R}_1}{\mathrm{R}_2} & =\frac{n_1^2}{n_2^2}=\frac{(2)^2}{(4)^2} \\ \therefore \quad \frac{\mathrm{R}_1}{\mathrm{R}_2} & =\frac{1}{4}=0.25 \end{aligned}$ (where, the symbols have their usual meanings)

Hence, the correct answer is option: 'A'.

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