Question

Let $v_1$ be the frequency of the series limit for Lyman series, $v_2$ the frequency of the first line of the Lyman series and $v_3$ the frequency of the series limit of Balmer series. Then which of the following relations is true?

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

Answer 1

Answer: (A)

$v_1-v_2=v_3$

Series limit means the shortest possible wavelength (maximum photon energy) and first line means the longest possible wavelength, (minimum photon energy) in the series
$v=c[\frac{1}{n^2}-\frac{1}{m^2}]$, where c is a constant.
For series limit of Lyman series $n=1m=\infty v_1=c$
For first line of Lyman series $n=1m=2v_2=\frac{3c}{4}$

For series limit of Balmer serles $n=2m=\infty v_3=\frac{c}{4}$
:. $v_1-v_2=v_3$

$E_1=E_2+E_3$
$h{V}_1=h{V}_2+h{V}_3$
$V_1=V_2+V_3$