Question

Q. How many photons of light having a wavelength 400 nm are necessary to provide 1 J of energy?

Q. A quantum of light having energy E has wavelength equal to 7200 A. Calculate the frequency of light which corresponds to energy equal to one quarter of E.

Answer 1

$$\begin{gathered} a)E=N\frac{hc}{\lambda } \\ 1=N\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{400\times {10}^{-9}} \\ N=\frac{400\times {10}^{-9}}{6.626\times {10}^{-34}\times 3\times {10}^8}=20.122\times {10}^{17}photons \\ b)E=\frac{hc}{\lambda }=h\nu \\ Since\frac{c}{\lambda }=\nu \\ Theenergycorrespondingtothewavelengthis7200A^0 \\ E=\frac{hc}{7200}---1 \\ \frac{E}{4}=\frac{hc}{\lambda }---2 \\ 1dividedby2 \\ \frac{E=\frac{hc}{7200}}{\frac{E}{4}=\frac{hc}{\lambda }} \\ \lambda =4\times 7200 \\ =28800A^0 \\ \frac{c}{\lambda }=\nu \\ \nu =\frac{3\times {10}^8}{28800\times {10}^{-10}}=1.042\times {10}^{14}Hz \end{gathered}$$