Electromagnetic Waves

JEE Main level, single correct, medium

138 of 165

Question 138 of 165

A monochromatic source of light operating at 1515 kW emits 2.5×10222.5\times 10^{22} photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ________. (Take h=6.6×10−34h=6.6\times 10^{-34} J·s and c=3×108c=3\times 10^8 m/s).

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Answer: (D) Ultraviolet

Power of the source, P=15 kW=15×103 J/sP = 15 \text{ kW} = 15 \times 10^3 \text{ J/s}

Number of photons emitted per second, n=2.5×1022 s−1n = 2.5 \times 10^{22} \text{ s}^{-1}

Energy of one photon, E=Pn=15×1032.5×1022=6×10−19 JE = \dfrac{P}{n} = \dfrac{15 \times 10^3}{2.5 \times 10^{22}} = 6 \times 10^{-19} \text{ J}

Using E=hcλE = \dfrac{hc}{\lambda}, we get λ=hcE\lambda = \dfrac{hc}{E}

λ=6.6×10−34×3×1086×10−19=3.3×10−7 m=330 nm\lambda = \dfrac{6.6 \times 10^{-34} \times 3 \times 10^8}{6 \times 10^{-19}} = 3.3 \times 10^{-7} \text{ m} = 330 \text{ nm}

The wavelength 330 nm330 \text{ nm} lies in the ultraviolet region of the electromagnetic spectrum.

Answer: Ultraviolet

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