The most probable radius (in pm) for finding the electron in `He^(+)` is.

Options

A. `0.0`
B. `52.9`
C. `26.5`
D. `105.8`

Explanation

To find the most probable radius for the electron in the helium ion \( He^+ \), we can use the formula derived from Bohr's model of the atom. The formula for the radius \( r \) in angstroms is given by:

\[ r = \frac{0.529 \, n^2}{Z} \]

Where:
- \( n \) is the principal quantum number (the shell number),
- \( Z \) is the atomic number of the element.

### Step 1: Identify the values of \( n \) and \( Z \)
For \( He^+ \):
- The atomic number \( Z \) for helium is 2.
- The electron in the \( He^+ \) ion is in the ground state, so \( n = 1 \).

### Step 2: Substitute the values into the formula
Now we can substitute \( n \) and \( Z \) into the formula:

\[ r = \frac{0.529 \, (1)^2}{2} \]

### Step 3: Calculate the radius in angstroms
Calculating this gives:

\[ r = \frac{0.529}{2} = 0.2645 \, \text{angstroms} \]

### Step 4: Convert angstroms to picometers
Since 1 angstrom is equal to \( 100 \, \text{pm} \):

\[ r = 0.2645 \, \text{angstroms} \times 100 = 26.45 \, \text{pm} \]

### Conclusion
Thus, the most probable radius for finding the electron in \( He^+ \) is approximately \( 26.45 \, \text{pm} \).

### Answer
The correct option is \( 26.5 \, \text{pm} \).