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What is the energy carried by a photon of frequency 6.0×10¹⁴ Hz?

Asked in GSEB Board July 2022 · Photon energy, momentum and mass

• (1) 3.98×10⁻¹⁹ J
• (2) 1.99×10⁻¹⁹ J
• (3) 3.98×10⁻¹⁷ J
• (4) 1.99×10⁻¹⁷ J

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives 1.99×10⁻¹⁹ J -- it is exactly half of hf, and a photon's energy is the whole of hf, with no factor 1/2. Sanity check: 6.63×10⁻³⁴×6.0×10¹⁴ = 3.98×10⁻¹⁹ J.
• (3) The power of ten is out by 10²: 10⁻³⁴×10¹⁴ = 10⁻²⁰, so the product is 39.8×10⁻²⁰ = 3.98×10⁻¹⁹ J, not 10⁻¹⁷.
• (4) No single slip gives 1.99×10⁻¹⁷ J: it is half of hf and a hundred times too large. A photon of 6×10¹⁴ Hz (visible light, about 500 nm) carries about 2.5 eV = 4×10⁻¹⁹ J.

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