Question

What is the energy of photons that corresponds to a wave number of $2.5\times {10}^{-5}c{m}^{-1}$?

• A. $2.5\times {10}^{-20}erg$
• B. $5.1\times {10}^{-23}erg$
• C. $5.0\times {10}^{-21}erg$
• D. $8.5\times {10}^{-2}erg$

Answer 1

The correct option is C $5.0\times {10}^{-21}erg$

We know that wave number is reciprocal of the wavelength.

Wave number $=\frac{1}{\lambda }=2.5\times {10}^{-5}c{m}^{-1}$

Speed of light ($c$ ) $=3\times {10}^{8}m{s}^{-1}$ $=$ $3\times {10}^{10}cm.s^{-1}$ and $h=6.626\times {10}^{-27}erg.s$

According to planck's theory, $E=\frac{hc}{\lambda }$$=6.626\times {10}^{-27}\times 3\times {10}^{10}\times 2.5\times {10}^{-5}$$=5.0\times {10}^{-21}erg$

Hence, the energy of photons is $5.0\times {10}^{-21}erg$.