What would be the radius of second orbit of `He^(+)` ion?

Options

A. ` 1.058 ` Å
B. ` 3.023 ` Å
C. 2.068 Å
D. 4.458 Å

Explanation

To find the radius of the second orbit of the \( \text{He}^+ \) ion using Bohr's model, we can follow these steps:

### Step 1: Understand the Formula
According to Bohr's model, the radius of the nth orbit for a hydrogen-like atom (or ion) is given by the formula:
\[ r_n = \frac{n^2}{Z} \times 0.592 \, \text{Å} \]
where:
- \( r_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (orbit number),
- \( Z \) is the atomic number of the ion,
- \( 0.592 \, \text{Å} \) is a constant.

### Step 2: Identify the Values
For the \( \text{He}^+ \) ion:
- The atomic number \( Z \) of helium is 2.
- We want to find the radius of the second orbit, so \( n = 2 \).

### Step 3: Substitute the Values into the Formula
Now we can substitute \( n \) and \( Z \) into the formula:
\[ r_2 = \frac{2^2}{2} \times 0.592 \, \text{Å} \]

### Step 4: Calculate
Calculating the values:
\[ r_2 = \frac{4}{2} \times 0.592 \, \text{Å} = 2 \times 0.592 \, \text{Å} = 1.184 \, \text{Å} \]

### Step 5: Final Answer
Thus, the radius of the second orbit of the \( \text{He}^+ \) ion is:
\[ r_2 = 1.184 \, \text{Å} \]