The energies E1 and E2of two radiations are 25 eV and 50 eV respectively. The relation            between their wavelengths. i.e. λ1 and λ2will be

# The energies ${\text{E}}_{\text{1}}{\text{\hspace{0.17em}and\hspace{0.17em}E}}_{\text{2}}$of two radiations are 25 eV and 50 eV respectively. The relation            between their wavelengths. $\text{i.e.\hspace{0.17em}}{\lambda }_{1}\text{\hspace{0.17em}}and\text{\hspace{0.17em}}{\lambda }_{2}$will be

1. A

${\lambda }_{1}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}2{\lambda }_{2}$

2. B

${\lambda }_{1}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}4{\lambda }_{2}$

3. C

${\lambda }_{1}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{1}{2}{\lambda }_{2}$

4. D

${\lambda }_{1}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{\lambda }_{2}$

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### Solution:

${\text{E}}_{\text{1}}{\text{\hspace{0.17em}=\hspace{0.17em}24\hspace{0.17em}eV,\hspace{0.17em}E}}_{\text{2}}\text{\hspace{0.17em}=\hspace{0.17em}50eV}$

${\text{E}}_{\text{1}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\text{hc}}{{\text{λ}}_{\text{1}}}{\text{\hspace{0.17em}and\hspace{0.17em}E}}_{\text{2}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{hc}}{{\text{λ}}_{\text{2}}}$

$\text{or\hspace{0.17em}}\frac{{\text{E}}_{\text{1}}}{{\text{E}}_{\text{2}}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{{\text{λ}}_{\text{2}}}{{\text{λ}}_{\text{1}}}\text{\hspace{0.17em}or\hspace{0.17em}}\frac{\text{25}}{\text{50}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{{\text{λ}}_{\text{2}}}{{\text{λ}}_{\text{1}}}{\text{\hspace{0.17em}or\hspace{0.17em}λ}}_{\text{1}}{\text{\hspace{0.17em}=\hspace{0.17em}2λ}}_{\text{2}}$

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