Question

The frequencies for series limit of Balmer and Paschen series respectively are ' $v_1$' and ' $v_3$'. If frequency of first line of Balmer series is '$v_2$' then the relation between '$v_1^{\prime }{,}^{\prime }{v}_2$' and '$v_3$' is

• A. $v_1-v_2=v_3$
• B. $v_1+v_3=v_2$
• C. $v_1+v_2=v_3$
• D. $v_1-v_3=2v_1$

Answer 1

Answer: (A)

Wavelength of Balmer series limit
$\frac{1}{{\lambda }_1}=R\left(\frac{1}{2^2}-\frac{1}{\infty }\right)$
Or $\frac{1}{{\lambda }_1}=\frac{R}{4}$
Using $c=v\lambda$
We get frequency for Balmer series limit $\frac{v_1}{c}=\frac{R}{4}$
$\Rightarrow v_1=\frac{Rc}{4}....$(1)
Wavelength of Paschen series limit $\frac{1}{{\lambda }_3}=R\left(\frac{1}{3^2}-\frac{1}{\infty }\right)$
Or $\frac{1}{{\lambda }_3}=\frac{R}{9}$
We get frequency for Paschen series limit $v_3=\frac{Rc}{9}\dots$ (2)
Wavelength of first line of Balmer series $\frac{1}{{\lambda }_2}=R\left(\frac{1}{2^2}-\frac{1}{3^2}\right)$
where $c=v_2{\lambda }_2$
$\Rightarrow v_2=\text{Rc}\left(\frac{1}{4}-\frac{1}{9}\right)\dots (3)$
From equations (1), (2) and (3) we get
$v_2=v_1-v_3$