Question

Find the energy of photon in each of the following:
A. Microwaves of wavelength $1.5cm$

B. Red light of wavelength $660nm$

C. Radiowaves of frequency $96MHz$

D. $X-$rays of wavelength $0.17nm$

Answer 1

(a) Energy of photon is given by the following relation

$E=\frac{hc}{\lambda }$

It is given that wavelength of microwave is

$\lambda =1.5cm=0.015m$

$E=\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{0.015}$

$E=1324\times {10}^{-26}J$

(b) Red light of wavelength 660 nm

$\lambda =660\times {10}^{-9}m$

$=\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{660\times {10}^{-9}}$

$=0.03\times {10}^{-17}J$

(c) Radio waves of frequency 96 MHz

$\nu =96\times {10}^{6}Hz$

$\lambda =\frac{1}{96\times {10}^6}$

$\lambda =0.0104\times {10}^{-6}m$

$E=\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{0.0104\times {10}^{-6}}$

$E=1909.6\times {10}^{-20}J$

(d) X− rays of wavelength 0.17 nm

$\lambda =0.17\times {10}^{-9}m$

$E=\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{0.17\times {10}^{-9}}$

$E=116.82\times {10}^{-17}J$