Question

Calculate the masses of photons corresponding to the first lines of Lyman and Balmer series of the atomic spectrum of hydrogen are in the ratio.

Answer 1

Since energy is directly proportional to mass and mass is inversely proportional to wavelength ($\lambda =\frac{h}{mv}$ Deleroglie's wavelength Equation)

Lyman Series: $\frac{1}{{\lambda }_1}=R_H(1-\frac{1}{4})=\frac{3R_H}{4}$ where $R_H$=Rydberg Constant

Balmer Series: $\frac{1}{{\lambda }_2}=R_H(\frac{1}{4}-\frac{1}{9})=\frac{5R_H}{36}$

${\lambda }_1:{\lambda }_2=\frac{5R_H}{36}\times \frac{4R_H}{3}=\frac{5}{27}{m}_1:m_2=27:5$