Q. $V_{1}$ is the frequency of the series limit of Lyman series, $V_{2}\ $is the frequency of the first line of Lyman series and $V_{3}$ is the frequency of the series limit of the Balmer series. Then
A) $v_{1} - v_{2}\ = \ v_{3}$
B) $v_{1} = \ v_{2} - v_{3}$
C) $\frac{1}{v_{2}} = \frac{1}{v_{1}} + \frac{1}{v_{3}}$
D) $\frac{1}{v_{1}} = \frac{1}{v_{2}} + \frac{1}{v_{3}}$
Explanation
(a) Frequency, $v = \ RC\left\lbrack \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right\rbrack$
$v_{1} = RC\left\lbrack 1 - \frac{1}{\infty} \right\rbrack$ =$RC$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v_{2} = RC\left\lbrack 1 - \frac{1}{4} \right\rbrack$ =$\frac{3}{4}RC$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v_{3} = RC\left\lbrack \frac{1}{4} - \frac{1}{\infty} \right\rbrack$ =$\frac{RC}{4}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v_{1} - \ v_{2}\ = \ v_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.