Question

The frequencies for series limit of Balmer and Paschen series respectively are ${}^{\prime }{v}_1^{\prime }$ and ${}^{\prime }{v}_3^{\prime }$. If frequency of first line of Balmer series is ${}^{\prime }{v}_2^{\prime }$ then the relation between ${}^{\prime }{v}_1^{\prime }{,}^{\prime }{v}_2^{\prime }$ and ${}^{\prime }{v}_3^{\prime }$ 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

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

Wavelength of Balmer series limit $\frac{1}{{\lambda }_1}=R(\frac{1}{2^2}-\frac{1}{\infty })$

Or $\frac{1}{{\lambda }_1}=\frac{R}{4}$

Using $c=\nu \lambda$

We get frequency for Balmer series limit $\frac{{\nu }_1}{c}=\frac{R}{4}$

$⟹$ ${\nu }_1=\frac{Rc}{4}$ .....(1)

Wavelength of Paschen series limit $\frac{1}{{\lambda }_3}=R(\frac{1}{3^2}-\frac{1}{\infty })$

Or $\frac{1}{{\lambda }_3}=\frac{R}{9}$

We get frequency for Paschen series limit ${\nu }_3=\frac{Rc}{9}$ .....(2)

Wavelength of first line of Balmer series $\frac{1}{{\lambda }_2}=R(\frac{1}{2^2}-\frac{1}{3^2})$ where $c={\nu }_2{\lambda }_2$

$⟹$ ${\nu }_2=Rc(\frac{1}{4}-\frac{1}{9})$ .....(3)

From equations (1), (2) and (3) we get ${\nu }_2={\nu }_1-{\nu }_3$