The ratio for the speed of the electron in the 3rd orbit of $He^+$ to the speed of the electron in the 3rd orbit of the hydrogen atom will be

2 : 1

The correct answer is Option (2) → 2 : 1

For a hydrogen-like ion, the speed of the electron in the nth orbit is given by:

$v_n = \frac{Z}{n} \cdot v_\text{H}$, where $v_\text{H}$ is the speed of electron in nth orbit of hydrogen atom.

Given:

He⁺ : Z = 2, n = 3

Hydrogen: Z = 1, n = 3

Ratio of speeds:

$\frac{v_\text{He⁺}}{v_\text{H}} = \frac{Z_\text{He⁺}/n_\text{He⁺}}{Z_\text{H}/n_\text{H}} = \frac{2/3}{1/3} = 2$

Answer: 2