Question

What is the wavelength of the radiation with photon energy which is the mean value of photon energies of radiations with wavelengths $\lambda_{1} = 4000\, \mathring{A} $ and $\lambda_{2} = 6000\, \mathring{A} $?

• A. $5000 \, \mathring{A} $
• B. $5200 \, \mathring{A} $
• C. $5600 \, \mathring{A} $
• D. $4800 \, \mathring{A} $

Answer 1

Answer: (D)

$\frac{hc}{\lambda_{3}} =\frac{\frac{hc}{\lambda_{1}}+\frac{hc}{\lambda_{2}}}{2}$
$\Rightarrow \frac{1}{\lambda_{3}} =\frac{1}{2} \left(\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}\right) $
$=\frac{1}{2} \left(\frac{1}{4000}+\frac{1}{6000}\right) $
$\Rightarrow \lambda_{3} =4800 \mathring{A} $