Question

In which of the following systems will the wavelength corresponding to n = 2 to n = 1 be minimum?

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

Answer 1

(d) Doubly ionized lithium

The wavelength corresponding the transition from n₂ to n₁ is given by
$\frac{1}{\lambda }=R{Z}^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$
Here,
R = Rydberg constant
Z = Atomic number of the ion

From the given formula, it can be observed that the wavelength is inversely proportional to the square of the atomic number.
Therefore, the wavelength corresponding to n = 2 to n = 1 will be minimum in doubly ionized lithium ion because for lithium, Z = 3.