The ratio between radii of `He^(+)` ion and `H` atom is

Options

A. `1`
B. `1/2`
C. `3/2`
D. `2`

Explanation

To find the ratio between the radii of the `He^(+)` ion and the `H` atom, we can use the formula for the radius of a hydrogen-like atom:

\[ r = \frac{0.52 \, n^2}{Z} \]

where:
- \( r \) is the radius,
- \( n \) is the principal quantum number,
- \( Z \) is the atomic number.

### Step 1: Identify the parameters for `He^(+)`
- For `He^(+)`, the electronic configuration is `1s^1`, which means it has one electron.
- The principal quantum number \( n \) for `He^(+)` is 1.
- The atomic number \( Z \) for helium is 2 (because it has 2 protons).

Using the formula:
\[ r_{He^+} = \frac{0.52 \times n^2}{Z} = \frac{0.52 \times 1^2}{2} = \frac{0.52}{2} = 0.26 \, \text{Å} \]

### Step 2: Identify the parameters for `H`
- For hydrogen (`H`), the electronic configuration is also `1s^1`.
- The principal quantum number \( n \) for `H` is 1.
- The atomic number \( Z \) for hydrogen is 1 (because it has 1 proton).

Using the formula:
\[ r_H = \frac{0.52 \times n^2}{Z} = \frac{0.52 \times 1^2}{1} = 0.52 \, \text{Å} \]

### Step 3: Calculate the ratio of the radii
Now, we can find the ratio of the radii of `He^(+)` to `H`:

\[ \text{Ratio} = \frac{r_{He^+}}{r_H} = \frac{0.26 \, \text{Å}}{0.52 \, \text{Å}} = \frac{1}{2} \]

### Final Answer
The ratio between the radii of `He^(+)` ion and `H` atom is \( \frac{1}{2} \).

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