Question

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

• A. $1:1.6$
• B. $1:2.6$
• C. $2.6:1$
• D. $1.6:1$

Answer 1

The correct option is D $1.6:1$

We know that, $c=\lambda v$
where, $c:$ speed of light; $v:$ frequency; $\lambda :$ wavelength
Since $c$ is constant, thus
$\frac{v_1}{v_2}=\frac{{\lambda }_2}{{\lambda }_1}$
Where, ${\lambda }_1:$ wavelength of violet light
${\lambda }_2:$ wavelength of red light
Now,
the energy associated with electromagnetic radiation is given by $E=hv$
Thus,
$\frac{E_1}{E_2}=\frac{v_1}{v_2}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{6.56\times {10}^{-5}\text{cm}}{4.10\times {10}^{-5}\text{cm}}=\frac{1.6}{1}$