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Energy of a photon is E = hf and its momentum is P = h/λ, where λ is the wavelength of the photon. With this assumption, the speed of the light wave is ______.

Asked in GSEB Board March 2018 · Photon energy, momentum and mass

• (1) P/E
• (2) E/P
• (3) EP
• (4) (E/P)²

Step-by-step solution

Why the other options are wrong

• (1) Upside down: P/E = h/λ·1/(hf) = 1/(fλ) = 1/c, the reciprocal of the speed, with unit s m⁻¹.
• (3) Multiplies where you must divide: EP = hf·h/λ = (h²f)/λ, whose unit J kg m s⁻¹ is not that of a speed.
• (4) (E/P)² = (fλ)² = c², the square of the speed of light, not the speed.

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