એક ઉદ્&zwj;ગમ S_1, પ્રતિ સેકન્ડે 50 | vedclass

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Question

For a source $S_{1}$

Wavelength, $\lambda_{1}=5000 \,\,{\mathop {	ext{A}}\limits^o }$

Number of photons emitted per second, $N_{1}=10^{15}$

Vedclass · Accepted Answer

$1$

Vedclass · Answer

For a source $S_{1}$

Wavelength, $\lambda_{1}=5000 \,\,{\mathop {	ext{A}}\limits^o }$

Number of photons emitted per second, $N_{1}=10^{15}$

Energy of each photon, $E_{1}=\frac{h c}{\lambda_{1}}$ 

Power of source $S_{1}, P_{1}=E_{1} N_{1}=\frac{N_{1} h c}{\lambda_{1}}$

For a source $S_{2}$ 

Wavelength, $\lambda_{2}=5100\,\,{\mathop {	ext{A}}\limits^o }$

Number of photons emitted per second,

$N_{2}=1.02 	imes 10^{15}$

Energy of each photon, $E_{2}=\frac{h c}{\lambda_{2}}$

Power of source $S_{2},\,\,P_{2}=N_{2} E_{2}=\frac{N_{2} h c}{\lambda_{2}}$

$	herefore \,\,\frac{{{	ext{ Power of}}\,{	ext{ }}{S_2}}}{{{	ext{ Power of }}\,{S_1}}} = \frac{{{P_2}}}{{{P_1}}}$ $ = \frac{{\frac{{{N_2}hc}}{{{\lambda _2}}}}}{{\frac{{{N_1}hc}}{{{\lambda _1}}}}} = \frac{{{N_2}{\lambda _1}}}{{{N_1}{\lambda _2}}}$

$ = \frac{{(1.02 	imes {{10}^{15}}{	ext{ photons/s) }} 	imes (5000{\mkern 1mu} {\mkern 1mu} \mathop {	ext{A}}\limits^o )}}{{({{10}^{15}}{	ext{ photons/s) }} 	imes (5100{\mkern 1mu} {\mkern 1mu} \mathop {	ext{A}}\limits^o )}}$ $ = \frac{{51}}{{51}} = 1$

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