A monochromatic source emits electromagnetic radiation with total power 15 kW at a rate of 2.5×10²² photons per second. Taking h = 6.6×10⁻³⁴ J·s and c = 3×10⁸ m·s⁻¹, in which region of the electromagnetic spectrum does the radiation lie?
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Question

A monochromatic source emits electromagnetic radiation with total power 15 kW at a rate of 2.5×10²² photons per second. Taking h = 6.6×10⁻³⁴ J·s and c = 3×10⁸ m·s⁻¹, in which region of the electromagnetic spectrum does the radiation lie?

Options

G1 Physics · Accepted Answer

Energy emitted per second is the source power: P = 15 kW = 15×10³ J·s⁻¹. If N photons are emitted each second, energy per photon is E(photon) = P ÷ N. Thus, E(photon) = 15×10³ ÷ (2.5×10²²) = 6×10⁻¹⁹ J. For a photon, E(photon) = hc ÷ λ. Therefore, λ = hc ÷ E(photon). Substitute: λ = [6.6×10⁻³⁴×3×10⁸] ÷ [6×10⁻¹⁹] = 3.3×10⁻⁷ m = 330 nm. A wavelength of about 330 nm lies in the ultraviolet region. Correct option: D.