Question:
The radius of the first orbit of \(\mathrm{He^+}\) is
The radius of the first orbit of \(\mathrm{He^+}\) is
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For hydrogen-like atoms:
- Radius decreases with increasing atomic number $Z$
- $r \propto \frac{1}{Z}$
Updated On: Apr 30, 2026
- $52.9$ pm
- $13.24$ pm
- $211.6$ pm
- $105.8$ pm
- $26.45$ pm
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The Correct Option is
Solution and Explanation
Concept:
Bohr radius for hydrogen-like atoms:
\[
r_n = \frac{n^2 a_0}{Z}
\]
where $a_0 = 52.9$ pm.
Step 1: Identify values.
\[ n = 1, \quad Z = 2 \; (\text{for He}^+) \]
Step 2: Substitute.
\[ r_1 = \frac{1^2 \times 52.9}{2} = 26.45\ \text{pm} \]
Step 1: Identify values.
\[ n = 1, \quad Z = 2 \; (\text{for He}^+) \]
Step 2: Substitute.
\[ r_1 = \frac{1^2 \times 52.9}{2} = 26.45\ \text{pm} \]
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