Question
A source $${S_1}$$ is producing, $${10^{15}}$$ photons/s of wavelength $$5000\,\mathop {\text{A}}\limits^ \circ .$$ Another source $${S_2}$$ is producing $$1.02 \times {10^{15}}$$ photons per second of wavelength $$5100\,\mathop {\text{A}}\limits^ \circ .$$ Then, $$\frac{{\left( {{\text{power}}\,{\text{of}}\,{S_2}} \right)}}{{\left( {{\text{power}}\,{\text{of}}\,{S_1}} \right)}}$$ is equal to
A.
1.00
B.
1.02
C.
1.04
D.
0.98
Answer :
1.00
Solution :
Number of photons emitted per second is given by
$$\eqalign{
& n = \frac{P}{{\left( {\frac{{hc}}{\lambda }} \right)}}\,\,\,\left[ {_{\frac{{hc}}{\lambda }\, = \,{\text{Energy}}}^{P\, = \,{\text{Power}}}} \right] \cr
& {\text{So,}}\,\,P = \frac{{nhc}}{\lambda } \cr} $$
So, for two different situations,
$$ \Rightarrow \frac{{{P_2}}}{{{P_1}}} = \frac{{{n_2}{\lambda _1}}}{{{n_1}{\lambda _2}}} = \frac{{1.02 \times {{10}^{15}} \times 5000}}{{{{10}^{15}} \times 5100}} = 1$$