Question

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

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

Answer 1

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

$\frac{1}{\lambda }=R(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
$f=\frac{C}{\lambda }=RC(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
${\nu }_1=RC(\frac{1}{1}-\frac{1}{{\infty }^2}){\nu }_1=RC(\frac{1}{1}-\frac{1}{2^2}){\nu }_3=RC(\frac{1}{2^2}-\frac{1}{{\infty }_2})$
$=RC$ $=\frac{3RC}{4}$ $=\frac{RC}{4}$
${\nu }_1={\nu }_2+r_3$