Question

If $\nu_{1}$ is the frequency of series limit of Lyman series, $\nu_{2}$ is the frequency of first line of Lyman series and $\nu_{3}$ be the frequency of the series limit of Balmer series. Then

• A. $\nu_{1}+\nu_{2}=\nu_{3}$
• B. $\nu_{2}-\nu_{1}=\nu_{3}$
• C. $\nu_{1}-\nu_{2}=\nu_{3}$
• D. $v_3=\frac{1}{2}\left(v_1+v_2\right)$

Answer 1

Answer: (C)

$ \begin{array}{l} v_1= cR \left(\frac{1}{1^2}-\frac{1}{\infty^2}\right)= cR \\ v_2= cR \left(\frac{1}{1^2}-\frac{1}{2^2}\right)=\frac{3 cR }{4} \\ v_3= cR \left(\frac{1}{2^2}-\infty\right)=\frac{ cR }{4} \end{array} $
So $v_1-v_2=v_3$