Question

What is the ratio of the energies of two radiations in which one has a wavelength of $6000\stackrel{\circ }{A}$ the other has a wavelength of $2000\stackrel{\circ }{A}$?

• A. $1:3$
• B. $1:2$
• C. $2:3$
• D. $2:1$

Answer 1

The correct option is A $1:3$

According to Planck's quantum theory $E=\frac{hc}{\lambda }$
Where, E = Energy of the radiation
h = Planck's constant $=6.626\times {10}^{-34}Js$
c = speed of light $=3\times {10}^{8}m/s$
$\lambda$ = wavelength of the radiation

Given: ${\lambda }_1=6000\stackrel{\circ }{A}$ and ${\lambda }_2=2000\stackrel{\circ }{A}$
$E_1=\frac{hc}{{\lambda }_1}....\left(i\right)$ and $E_2=\frac{hc}{{\lambda }_2}....\left(ii\right)$
Dividing equation (i) with equation (ii)
$\frac{E_1}{E_2}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{2000}{6000}=\frac{1}{3}$

So,
$E_2=3E_1$
Hence, the ratio of energy between the two radiations is $1:3$.