question_answer

Calculate the energy in joule corresponding to light of wavelength 45 nm : (Planck's constant \[h=6.63\times {{10}^{-34}}\] is;   speed   of   light\[c=3\times {{10}^{8}}m{{s}^{-1}})\]                                                   [AIPMT 2014]

A)  \[6.67\times {{10}^{15}}\]       

B)       \[6.67\times {{10}^{11}}\]

C)  \[4.42\times {{10}^{-15}}\]       

D)       \[4.42\times {{10}^{-18}}\]

Correct Answer: D Solution : The wavelength of light is related to its energy by the equation, \[E=\frac{hc}{\lambda }.\]

Given, \[\lambda =45nm=45\times {{10}^{-9}}m\]

\[[\because \,1nm={{10}^{-9}}m]\]

Hence, \[E=\frac{6.63\times {{10}^{-34}}js\times 3\times {{10}^{8}}m{{s}^{-1}}}{45\times {{10}^{-9}}m}\]

\[=4.42\times {{10}^{-18}}\text{J}\]

Hence, the energy corresponds to light of wavelength 45 nm is \[4.42\times {{10}^{-18}}J.\]