Question

In which of the following systems will the radius of the first orbit (n = 1) be minimum?

(a) Hydrogen atom
(b) Deuterium atom
(c) Singly ionized helium
(d) Doubly ionized lithium

Answer 1

(d) Doubly ionized lithium

For a hydrogen-like ion with Z protons in the nucleus, the radius of the nth state is given by

$r_{\mathrm{n}}=\frac{n^2{a}_0}{Z}$

Here, a₀ = 0.53 pm

For lithium,
Z = 3
Therefore, the radius of the first orbit for doubly ionised lithium will be minimum.