Structure of Atom - Result Question 4
####4. 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: [2011]
(a) $\lambda_1=\lambda_2$
(b) $\lambda_1=2 \lambda_2$
(c) $\lambda_1=4 \lambda_2$
(d) $\lambda_1=\frac{1}{2} \lambda_2$
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Solution:
- (b) Given $E_1=25 eV \quad E_2=50 eV$
$ \begin{aligned} & E_1=\frac{h c}{\lambda_1} \quad E_2=\frac{h c}{\lambda_2} \quad \therefore \frac{E_1}{E_2}=\frac{\lambda_2}{\lambda_1} \\ & \therefore \frac{\lambda_2}{\lambda_1}=\frac{25}{50}=\frac{1}{2} \quad \therefore \lambda_1=2 \lambda_2 \end{aligned} $
