MHT CET · Physics · Atomic 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 \(2: 1\)
- C \(1: 4\)
- D \(1: 2\)
Answer & Solution
Correct Answer
(C) \(1: 4\)
Step-by-step Solution
Detailed explanation
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,
\(\begin{aligned}
& \frac{\mathrm{r}_1}{\mathrm{r}_2}=\left(\frac{1}{2}\right)^2 \times \frac{\mathrm{r}_0}{\mathrm{r}_0} \\
& \therefore \quad \frac{r_1}{r_2}=\frac{1}{4}
\end{aligned}\)
\(\begin{aligned}
& \frac{\mathrm{r}_1}{\mathrm{r}_2}=\left(\frac{1}{2}\right)^2 \times \frac{\mathrm{r}_0}{\mathrm{r}_0} \\
& \therefore \quad \frac{r_1}{r_2}=\frac{1}{4}
\end{aligned}\)
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