Question

Match each List - I with an appropriate pair of characteristics from List - II and select the correct answer using the code given below the lists.

$\begin{array}{cc}List-I& List-II\\ \text{(I) Lyman series}& \text{(P) maximum number of spectral line observed = 6}\\ \text{(II) Balmer series}& \left(Q\right)\text{maximum number of spectral line observed = 2}\\ \text{(III) In a sample of}H\text{-atom for 5 upto}& \left(R\right)2^{nd}\text{~line has wave number}\frac{8R}{9}\\ \text{2 transition}& \\ \text{(IV) In a single isolated}H\text{-atom for}& \text{(S)}{2}^{nd}\text{line has wave number}\frac{3R}{16}\\ \text{3 upto 1 transition}& \\ & \text{(T) Total number of spectral line is 10}\\ & \text{(U) Hydrogen spectral series}\end{array}$

• A. (I - S, U), (II - R, U), (III - Q), (IV - T)
• B. (I - R, U), (II - S, T), (III - P), (IV - U)
• C. (I - R, U), (II - S, U), (III - P, U), (IV - Q, U)
• D. (I - R, S), (II - S, T), (III - U), (IV - Q)

Answer 1

The correct option is C (I - R, U), (II - S, U), (III - P, U), (IV - Q, U)

(I) For Lyman series, $\overline{v}$ for second line $(3\to 1)=R(1{)}^2[\frac{1}{1^2}-\frac{1}{3^2}]=\frac{8R}{9}$
(II) For Balmer series, $\overline{v}$ for second line $4\to 2=R(1{)}^2[\frac{1}{2^2}-\frac{1}{4^2}]=\frac{3R}{16}$
(III) In a sample of $H$-atom for $5\to 2$ transition, maximum number of spectral lines observed $=\frac{(5-2)(5-2+1)}{2}=6$
(IV) In a single isolated $H$-atom for $3\to 1$ transition, maximum number of spectral lines observed $=2(3\to 2,2\to 1)$