The ratio of the power of a light source S_1 to that the light source S_2 is 2 . S_1 is emitting 2 × 10^ 15 photons per second at 600 nm . If the wavelength of the source S_2 is 300 nm , then the number of photons per

Correct answer: 5 Since power emitting by a source is given as aligned & = Total energy emitted time & = (E_1 photon ) × Number of photons (N) t & P_1=(E_1) n aligned aligned & P_1 P_2 = (E_1) n_1 (E_2) n_2 = ( hC λ_1 ) n_1 ( hC λ_2 ) n_2 & P_1 P_2 =((λ_2)/(λ_1)) n_1 n_2 aligned Substituting the given values aligned & 2=((300)/(600)) × 2 × 10^ 15 n_2 & n_2=(1)/(2) × 10^ 15 =5 × 10^ 14 Photon / sec aligned

JEE Main 202524 JanuaryEvening Shift

Exam: JEE Main
Year: 2025
Date: 24 January
Shift: Evening Shift
Subject: Physics
Chapter: Wave Optics

JEE Main 2025 · 24 January · Evening Shift · Physics · Wave Optics

The ratio of the power of a light source S_1 to that the light...

The ratio of the power of a light source

S_1

to that the light source

S_2

2 . S_1

is emitting

2 \times 10^{15}

photons per second at 600 nm . If the wavelength of the source

S_2

is 300 nm , then the number of photons per second emitted by

S_2

\ldots\ldots

\times 10^{14}

Correct answer

Step-by-step solution

Since power emitting by a source is given as

\begin{aligned} & =\frac{\text{ Total energy emitted }}{\text{ time }} \\ & =\frac{\left(E_1 \text{ photon }\right) \times \text{ Number\text{ of } photons }(N)}{t} \\ & P_1=\left(E_1\right) n \end{aligned}

\begin{aligned} & \frac{\mathrm{P}_1}{\mathrm{P}_2}=\frac{\left(\mathrm{E}_1\right) \mathrm{n}_1}{\left(\mathrm{E}_2\right) \mathrm{n}_2}=\frac{\left(\frac{\mathrm{hC}}{\lambda_1}\right) \mathrm{n}_1}{\left(\frac{\mathrm{hC}}{\lambda_2}\right) \mathrm{n}_2} \\ & \frac{\mathrm{P}_1}{\mathrm{P}_2}=\left(\frac{\lambda_2}{\lambda_1}\right) \frac{\mathrm{n}_1}{\mathrm{n}_2} \end{aligned}

Substituting the given values

\begin{aligned} & 2=\left(\frac{300}{600}\right) \times \frac{2 \times 10^{15}}{\mathrm{n}_2} \\ & \mathrm{n}_2=\frac{1}{2} \times 10^{15}=5 \times 10^{14} \text{ Photon } / \mathrm{sec} \end{aligned}

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