Q118 / 150 · MHT CET 2024 (03 May Shift 2) · Physics

The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is

  • A
    $4: 1$
  • B
    $2: 1$
  • Correct answer
    C
    $1: 4$
  • D
    $1: 2$

Solution

Radius of $\mathrm{n}^{\text {th }}$ Bohr orbit, $\mathrm{r}_{\mathrm{n}}=\mathrm{n}^2 \mathrm{r}_0$ Ratio of first Bohr orbit to second Bohr orbit, $\begin{aligned} & \frac{\mathrm{r}_1}{\mathrm{r}_2}=\left(\frac{1}{2}\right)^2 \times \frac{\mathrm{r}_0}{\mathrm{r}_0} \\ & \therefore \quad \frac{r_1}{r_2}=\frac{1}{4} \end{aligned}$

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

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