Question

Find the ratio of frequencies of violet light $({\lambda }_1=4.10\times {10}^{-5}cm)$ to that of red light $({\lambda }_2=6.56\times {10}^{-5}cm)$. Also determine the ratio of energies carried by them.

• A. 2 : 1
• B. 1 : 2
• C. 1.6 : 1
• D. 2.3 : 1

Answer 1

The correct option is C

1.6 : 1

We know,
$c=\nu \lambda$
$\Rightarrow \nu$ is inversely proportional to $\lambda$

Now, using $c=\nu \lambda$,
Where $c$ is speed of light, $\nu$ is frequency, $\lambda$ is wavelength

$\frac{v_1}{v_2}=\frac{{\lambda }_2}{{\lambda }_1}$[1:violet and 2:red]

$\Rightarrow \frac{v_1}{v_2}=\frac{6.56\times {10}^{-5}}{4.10\times {10}^{-5}}=1.6:1$

Now the energy associated with electromagnetic radiation is given by $E=h\nu$. Therefore,
$\frac{E_1}{E_2}=\frac{v_1}{v_2}=\frac{{\lambda }_2}{{\lambda }_1}=1.6:1$
Hence, the ratio of energies is same as that of frequencies.