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)

$\frac{hc}{{\lambda }_3}=\frac{\frac{hc}{{\lambda }_1}+\frac{hc}{{\lambda }_2}}{2}$
$\Rightarrow \frac{1}{{\lambda }_3}=\frac{1}{2}\left(\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}\right)$
$=\frac{1}{2}\left(\frac{1}{4000}+\frac{1}{6000}\right)$
$\Rightarrow {\lambda }_3=4800\mathring{A}$