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Q)

Given the $\lambda$ values for violet light ($\lambda=4.10\times 10^{-5}cm)$ and red light($\lambda=6.56\times 10^{-5}cm$), which of the following is true about the ratio of energies carried by them and their frequencies?

$\begin{array}{1 1}(a)\;\text{ratio of energy & frequency is different}\\(b)\;\text{ratio of energy is 1/4 as that of frequency}\\(c)\;\text{ratio of energy is same as that of frequency}\\(d)\;\text{ratio of energy is double as that of frequency}\end{array}$

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A)
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Using, $c=\nu\lambda$
Let, $\nu _1$ be the frequency of the Red light.
$\lambda _1$ be the wavelength of the Red light.
$\nu _2$ be the frequency of the Violet light.
$\lambda _2$ be the wavelength of the Violet light.
Since, $\large\nu \propto \frac{1}{\lambda};\;\;\;\;\large\frac{\nu _1}{\nu _2}=\frac{\lambda_2}{\lambda_1}$
$\large\frac{\nu _1}{\nu _2}=\frac{4.10\times 10^{-5}}{6.56\times 10^{-5}}$$ = 0.625$
Now the energy associated with electromagnetic radiation is given by $E=h\nu$
$=\large\frac{E_1}{E_2}=\large\frac{\nu_1}{\nu_2}=\frac{\lambda_1}{\lambda_2}$$=0.625$
$\therefore$ Hence the ratio of energies is same as that of the frequencies
Hence (c) is the correct answer.
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