Question

A sample of ${He}^{+}$ ions in a gaseous state had all ions in $n^{th}$ excited state. This sample on returning to ground state emits a total of 28 spectral lines. Value of $n$ is:

• A. 8
• B. 7
• C. 6
• D. 5

Answer 1

Answer: (A)

8

Possible spectral lines $=\frac{(n_2-n_1)(n_2-n_1+1)}{2}$

$n_1=1$

$n_2=n$

Substituting the values, we get-

$\frac{n(n-1)}{2}=28$

$n(n-1)=2\times 28=56$

$n^2-n=56$

$n=8$