Question

Let $v_1$ be the frequency of the series limited of the Lyman series, $v_2$ be the frequency of the first line of the Lyman series, and $v_3$ be the frequency of the series limited of the Balmer series. Then:

• A. $v_1-v_2=v_3$
• B. $v_2-v_1=v_3$
• C. $v_3=\frac{1}{2}(v_1+v_3)$
• D. $v_1+v_2=v_3$

Answer 1

The correct option is A $v_1-v_2=v_3$

From Rydberg's relation:

$\frac{1}{\lambda }=R_H(\frac{1}{n_1^2}-\frac{1}{n_2^2})$

$⟹\nu =R_{H}c(\frac{1}{n_1^2}-\frac{1}{n_2^2})$

First line of lyman series is from transition $2\to 1$

Series limit of lyman is from transition $\infty \to 1$

Series limit of balmer is from transition $\infty \to 2$

${\nu }_1=R_{H}c(1-\frac{1}{{\infty }^2})$

${\nu }_2=R_{H}c(1-\frac{1}{2^2})$

${\nu }_3=R_{H}c(\frac{1}{2^2}-\frac{1}{{\infty }^2})$

${\nu }_1-{\nu }_2=R_{H}c(\frac{1}{2^2}-\frac{1}{{\infty }^2})={\nu }_3$