Question

Monochromatic radiations of wavelength $\lambda$ are incident on a hydrogen sample in the ground state. Hydrogen atom absorbs the light and subsequently emits radiations of $10$ different wavelengths. The value of $\lambda$ is nearly

• A. $203nm$
• B. $95nm$
• C. $80nm$
• D. $73nm$

Answer 1

The correct option is B $95nm$

Total no. of wavelengths emitted $={}^n{C}_2=\frac{n(n-1)}{2}$
${}^n{C}_2=10$
$n^2-n-20=0$
$n=-4or5$
$n=5$

So the energy required:
$\frac{1}{\lambda }=R(1-\frac{1}{5^2})$
$R=1.1\times {10}^7$
$\lambda =94.6nm$