The ratio of the power of a light source S₁ to that of the light source S₂ is 2. S₁ is emitting 2 × 10¹⁵ photons per second at 600 nm. If the wavelength of the source S₂ is 300 nm, then the number of photons per second emitted by S₂ is __________ × 10¹⁴. Numerical answer type. Work it out, then open the answer.

Answer: 5. P = n(hc)/(λ) ⇒ n = (Pλ)/(hc), so (n₁)/(n₂) = (P₁)/(P₂)·(λ₁)/(λ₂) (n₁)/(n₂) = 2×(600)/(300) = 4 n₂ = 2×10¹⁵4 = 5×10¹⁴ per second So the answer is 5.

The ratio of the power of a light source S₁ to that of the light… | JEE Main 2025 (24 Jan, Shift 2)

Q7JEE Main 2025 · 24 JAN · SHIFT 2Medium

Photons: Energy, Momentum & Radiation Pressure

The ratio of the power of a light source $S_1$ to that of the light source $S_2$ is $2.\ S_1$ 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 $S_2$ is __________ $\times 10^{14}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 5

$P = n\dfrac{hc}{\lambda} \Rightarrow n = \dfrac{P\lambda}{hc}$ , so $\dfrac{n_1}{n_2} = \dfrac{P_1}{P_2}\cdot\dfrac{\lambda_1}{\lambda_2}$
$\dfrac{n_1}{n_2} = 2\times\dfrac{600}{300} = 4$
$n_2 = \dfrac{2\times10^{15}}{4} = 5\times10^{14}$ per second
So the answer is $5$ .

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