Question

The energies $E_1$ and $E_2$ of two radiations are $25\, eV$ and $50 \,eV$, respectively. The relation between their wavelengths i.e., $\lambda_{1}$ and $\lambda_{2}$ will be :

• A. $\lambda_{1} = \lambda_{2}$
• B. $\lambda_{1} = 2\lambda_{2}$
• C. $\lambda_{1} = 4\lambda_{2}$
• D. $\lambda_{1} = \frac{1}{2}\lambda_{2}$

Answer 1

Answer: (B)

Given $E_1 = 25\,eV $
$E_2 = 50\, eV$
$E_{1} = \frac{hc}{\lambda_{1}} \,E_{2} = \frac{hc}{\lambda _{2}} $
$\therefore \frac{E_{1}}{E_{2}} = \frac{\lambda _{2}}{\lambda _{1}}$
$\therefore \frac{\lambda _{2}}{\lambda _{1}} = \frac{25}{50} = \frac{1}{2} $
$\lambda _{1} = 2\lambda _{2}$