Question

Ratio of wavelength of photon corresponding to $\beta$-line of Lyman series and $\gamma$-line of Paschen series for a $H-$atom is:

• A. $2/3$
• B. $1/4$
• C. $3/32$
• D. $4/1$

Answer 1

Answer: (C)

$3/32$

lyman series $\alpha$ line = 2$\to$1 transition

$\beta$ line = 3$\to$1 transition

paschen series $\alpha$ line = 4$\to$3transition

$\beta$ line = 5$\to$3 transition

$\gamma$ line = 6$\to$3transition

wavelength inversly varies to $\frac{1/n_1-1/n_2}{1/n_1-1/n_2}$

$\frac{\beta \text{line of lyman series (wavelength)}}{\alpha \text{line of paschen series(wavelength)}}=\frac{1/3^2-1/6^2}{1/1-1/3^2}$

$=\frac{3/36}{8/9}$

$=3/32$