Question

Suggest two transitions in the atomic spectrum of hydrogen for which the wave number ratio is $108:7$

• A. First Lyman and first Brackett transition
• B. First and second Lyman series transition
• C. First Lyman and first Balmer transition
• D. First Lyman and first Paschen transition

Answer 1

Answer: (D)

$\bar{v}=R_H\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$

For first Lyman transition,

$\bar{v}=R_H\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=\frac{3}{4}{R}_H$

For first Balmer transition,

$\bar{v}=R_H\left(\frac{1}{2^2}-\frac{1}{3^2}\right)=\frac{5}{36}{R}_H$

For first Paschen transition,

$\bar{v}=R_H\left(\frac{1}{3^2}-\frac{1}{4^2}\right)=\frac{7}{144}{R}_H$

For first Brackett transition,

$\bar{v}=R_H\left(\frac{1}{4^2}-\frac{1}{5^2}\right)=\frac{9}{400}{R}_H$

Lyman : Paschen $=\frac{3}{4}:\frac{7}{144}=3:$

$\frac{7}{36}=108:7$