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Monochromatic light of frequency 6×10¹⁴ Hz is produced by a laser. The power emitted is 2×10⁻³ W. The energy of a photon in this light beam is ______ eV. [h = 6.63×10⁻³⁴ J s, 1 eV = 1.6×10⁻¹⁹ J]

Asked in GSEB Board March 2023 · Photon energy, momentum and mass

• (1) 3.0
• (2) 3.5
• (3) 4.0
• (4) 2.5

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 3.0 eV; a photon of that energy would need a frequency of about 7.2×10¹⁴ Hz. Sanity check: (hf)/e = (3.98×10⁻¹⁹)/(1.6×10⁻¹⁹) = 2.49 eV.
• (2) No single slip gives 3.5 eV (it would need about 8.4×10¹⁴ Hz). Note that the beam's power plays no part in the energy of one photon.
• (3) 4.0 is the photon energy in units of 10⁻¹⁹ J (hf = 3.98×10⁻¹⁹ J) -- the final division by 1.6×10⁻¹⁹ to convert joule to eV was skipped.

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