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Chemistry Question on Structure of atom

Calculate the energy in joule corresponding to light of wavelength 45 nm (Planck's constant, h=6.63×10−34h=6.63\times10^{-34} Js; speed of light, c=3×108c=3\times 10^{8}.

A

6.67×10156.67\times10^{15}

B

6.67×10116.67\times10^{11}

C

6.63×10−156.63\times10^{-15}

D

4.42×10−184.42\times10^{-18}

Answer

4.42×10−184.42\times10^{-18}

Explanation

Solution

The wavelength of light is related to its energy by the equation, E=hcλ.(E=hv)E=\frac{hc}{\lambda}.(E=hv) Given, λ=45nm=45×10−9m[∵1nm=10−9m]\lambda=45nm=45\times10^{-9}m [\because 1nm =10^{-9}m] Hence, E=6.63×10−34Js×3×108ms−145×10−9mE=\frac{6.63\times10^{-34}Js\times3\times10^{8}ms^{-1}}{45\times10^{-9}m} =4.42×10−18J=4.42 \times10^{-18} J
Hence, the energy corresponds to light of wavelength 45 nm is4.42×10−18J45 \,nm \,is 4.42\times10^{-18}J