Question

The frequency for a series limit of Balmer and Paschen series respectively are $f_1^{}$ and $f_3^{}$. If the frequency of the first line of Balmer series is $f_2^{}$ then the relation between${ }^{}{f}_1^{}, f_2^{}$ and $f_3^{}$ is

• A. $f_1-f_2=f_3$
• B. $f_1+f_3=f_2$
• C. $f_1+f_2=f_3$
• D. $f_2-f_3=2f_1$

Answer 1

Answer: (A)

$c=f\lambda ,\frac{1}{\lambda }=\frac{f}{c}$
$\frac{1}{\lambda }=R\left(\frac{1}{P^2}-\frac{1}{n^2}\right)$
$\Rightarrow f=Rc\left(\frac{1}{P^2}-\frac{1}{n^2}\right)$
$\Rightarrow f_2=Rc\left(\frac{1}{2^2}-\frac{1}{3^2}\right)=Rc\left(\frac{1}{4}-\frac{1}{9}\right)=\frac{5Rc}{36}$
$f_1=Rc\left(\frac{1}{2^2}\right)=\frac{Rc}{4}$
$f_3=Rc\left(\frac{1}{3^2}\right)=\frac{Rc}{9}$
$\therefore f_1-f_3=Rc\left(\frac{1}{4}-\frac{1}{9}\right)$
$\therefore f_1-f_3=f_2$
$\therefore f_1-f_2=f_3$