Question

Calculate the energy in joule corresponding to light of wavelength $45\, nm$ (Planck's constant, $h=6.63\times10^{-34} \,Js$; speed of light, $c=3\times 10^{8}\,ms^{-1}$).

• A. $6.67\times10^{15}$
• B. $6.67\times10^{11}$
• C. $6.63\times10^{-15}$
• D. $4.42\times10^{-18}$

Answer 1

Answer: (D)

The wavelength of light is related to its energy by the equation, $E=\frac{h c}{\lambda},(E=h v)$
Given, $\lambda=45 nm =45 \times 10^{-9} m \left[\because 1 nm =10^{-9} m \right]$
Hence, $E =\frac{6.63 \times 10^{-34} Js \times 3 \times 10^{8} m s ^{-1}}{45 \times 10^{-9} m } $
$=4.42 \times 10^{-18} J$
Hence, the energy corresponds to light of wavelength $45 nm$ is $4.42 \times 10^{-18} J$.