Discussion Forum

The frequencies for series limit of Balmer and P aschen series respectively are 'v₁' and 'v₃' .If frequency of first line of Balmer series is 'v2' then the relation between 'v₁'. 'v₂' and 'v₃' is 

Answer:

Explanation:

 As we know, v= n$\lambda$

$\Rightarrow $   $\frac{1}{\lambda}=\frac{n}{v}\Rightarrow \frac{1}{\lambda}=R\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$

$\Rightarrow $      $v=Rc\left(\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{2}}\right)$

$\therefore$   

$v_{2}=Rc\left(\frac{1}{2^{2}}-\frac{1}{3^2}\right)=Rc\left(\frac{1}{4}-\frac{1}{9}\right)$ .....(i)

$v_{1}=Rc\left(\frac{1}{2^{2}}\right)=\frac{Rc}{4}$

 $v_{3}=Rc\left(\frac{1}{3^{2}}\right)=\frac{Rc}{9}$

 $\Rightarrow$        $v_{1}-v_{3}=Rc\left(\frac{1}{4}-\frac{1}{9}\right)$  ......(ii)

 From Eqs.(i) and (ii), we get

    v₁ -v₃  =v₂

 $\Rightarrow$      $v_{1}-v_{2}=v_{3}$