Q. The wavelength of a spectral line emitted by hydrogen atom in the Lyman series is$\frac{16}{15R}cm$. What is the value of $n_{2}?$($R$=Rydberg constant)
A) 2
B) 3
C) 4
D) 1
Explanation
(c)
For Lyman series,
$\frac{1}{\lambda} = R\left\lbrack \frac{1}{1^{2}} - \frac{1}{n_{2}^{2}} \right\rbrack$
$\frac{15R}{16} = R\left\lbrack \frac{1}{1^{2}} - \frac{1}{n_{2}^{2}} \right\rbrack$
$\frac{15R}{16R} = \left\lbrack \frac{n_{2}^{2} - 1}{n_{2}^{2}} \right\rbrack$
$\frac{15}{16} = \frac{n_{2}^{2} - 1}{n_{2}^{2}}$
$15n_{2}^{2} = 16n_{2}^{2} - 16\$
$n_{2}^{2} = 16,\ n_{2} = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.