question_answer

\[\text{3}\times \text{1}{{0}^{\text{18}}}\]photons of a certain light radiation are found to produce 1.5 J of energy. Calculate the wavelength of light radiations, (\[\text{h}=\text{6}.\text{63}\times \] \[\text{1}{{0}^{-\text{34}}}\] Js).

Answer:

Number of photons \[(n)=3\times {{10}^{18}}\] Energy \[(E)=1.5\text{ }J\] Wavelength\[(\lambda )~=?\] \[h=6.63\times {{10}^{34}}JS\] \[E=\frac{nhc}{\lambda }\] \[\Rightarrow \] \[\lambda =\frac{nhc}{E}=\frac{3\times {{10}^{18}}\times 6.63\times {{10}^{-34}}\times 3\times {{10}^{8}}}{1.5}\]                 \[=39.78\times {{10}^{8}}m\](or) \[3978\times {{10}^{10}}m=3978\overset{{}^\circ }{\mathop{\text{A}}}\,\]