In a mixture of `H- He^(+)` gas (`He+ `is singly ionized He atom), `H` atom and `He+` ions are excited to their respective first excited state. Subsequently `H` atoms transfer their total excitation energy to `He+` ions (by collisions) Assume that the bohr model of atom is exactly valid.
The ratio of the kinetic energy of the `n = 2` electron for the `H` atom to the of `He^(+)` lon is -

Options

A. `(1)/(4)`
B. `(1)/(2)`
C. 1
D. 2

Explanation

To solve the problem, we need to find the ratio of the kinetic energy of the n = 2 electron in a hydrogen atom (H) to that of a singly ionized helium ion (He⁺). We will use the Bohr model of the atom to calculate the kinetic energies.

### Step-by-Step Solution:

1. **Kinetic Energy Formula**:
The kinetic energy (K.E.) of an electron in a hydrogen-like atom can be given by the formula:
\[
K.E. = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2}
...