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
Answer & explanation
Correct answer: option 2
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