Question

Calculate the radius of the second orbit of \(He^{+}\).

• A. 52.9 Pm
• B. 105.8 Pm
• C. 158.7 Pm
• D. 211.6 Pm

Hint:

Use r = 52.9 pm x n^2 / Z for a hydrogen-like ion.

Answer 1

The Correct Option is B

Step 1: Formula First
$ r_n = a_0\,\frac{n^2}{Z} $ with $ a_0 = 52.9 $ pm.

Step 2: Calculation
$ r_2 = \frac{52.9\times 2^2}{2} = 52.9\times 2 $.

Step 3: Result
$ r_2 = 105.8 $ pm, option (B).

Final Answer:
Substituting n = 2 and Z = 2 gives 105.8 pm. \[ \boxed{\text{(B) }105.8\ \text{pm}} \]