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If the energy of a photon of wavelength 6000 A is 3.2×10⁻¹⁹ J, the energy of a photon of wavelength 4000 A will be ______.

Asked in GUJCET 2018 · Photon energy, momentum and mass

• (1) 4.44×10⁻¹⁹ J
• (2) 2.22×10⁻¹⁹ J
• (3) 1.11×10⁻¹⁹ J
• (4) 4.80×10⁻¹⁹ J

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 4.44×10⁻¹⁹ J. The direction is right (shorter wavelength, more energy), but E ∝ 1/λ fixes the factor at (6000)/(4000) = 1.5.
• (2) No single slip gives 2.22×10⁻¹⁹ J; even the common slip E ∝ λ gives 3.2×(4000)/(6000) = 2.13×10⁻¹⁹ J. A shorter wavelength must carry more energy, not less.
• (3) No single slip gives 1.11×10⁻¹⁹ J, and it is below 3.2×10⁻¹⁹ J, so it has the change in the wrong direction: since E = (hc)/λ, a shorter wavelength means more energy.

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