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Monochromatic light of frequency 6 × 10¹⁴ Hz is produced by a laser. The power emitted is 4 × 10⁻³ W. How many photons per second on an average are emitted by the source? [h = 6.63 × 10⁻³⁴ Js]

Asked in GUJCET 2025 · Counting photons

• (1) 1 × 10¹⁶ Photons per second
• (2) 5 × 10¹⁶ Photons per second
• (3) 3 × 10¹⁵ Photons per second
• (4) 5 × 10¹⁵ Photons per second

Step-by-step solution

Why the other options are wrong

• (2) No single slip produces 5×10¹⁶ per second: that rate would need each photon to carry only 8×10⁻²⁰ J, a fifth of the real 3.98×10⁻¹⁹ J. Sanity check: n = P/(h u) = (4×10⁻³)/(3.98×10⁻¹⁹) = 1.0×10¹⁶ per second.
• (3) No single slip produces 3×10¹⁵ per second: that rate would need a photon energy of 1.3×10⁻¹⁸ J, more than three times the real one. Sanity check: sharing 4×10⁻³ J each second among photons of 3.98×10⁻¹⁹ J takes 1.0×10¹⁶ of them.
• (4) 5×10¹⁵ is the answer to the NCERT worked example, where a laser of this same frequency emits 2.0×10⁻³ W. This laser emits 4×10⁻³ W, twice the power, so it sends out twice as many photons each second.

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