Question

The masses of photons corresponding to the first line of Bracket and the Balmer series of the atomic hydrogen are in the ratio of:

• A. $5/27$
• B. $\frac{1}{320}$
• C. $\frac{81}{500}$
• D. $\frac{500}{81}$

Answer 1

Answer: (C)

$\frac{81}{500}$

As we know,
$\lambda =h/mc$
$m=\frac{h}{c\lambda }$
also,
$1/\lambda =R{Z}^2(1/n_1^2-1/n_2^2)$
$\therefore \frac{m_{Brack}}{m_{Bal}}=\frac{{\lambda }_{Bal}}{{\lambda }_{Brack}}=\frac{R_H\left[\frac{1}{4^2}-\frac{1}{5^2}\right]}{R_H\left[\frac{1}{2^2}-\frac{1}{3^2}\right]}=\frac{81}{500}$