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The frequency of a photon having energy 100 eV is ______ Hz. (Take h = 6.62×10⁻³⁴ J s; 1 eV = 1.6×10⁻¹⁹ J)

Asked in GUJCET 2011 · Photon energy, momentum and mass

• (1) 2.417×10⁻¹⁶
• (2) 2.417×10¹⁶
• (3) 2.417×10¹⁷
• (4) 10.54×10¹⁷

Step-by-step solution

Why the other options are wrong

• (1) The digits are right but the power of ten has the wrong sign. Dividing by h ≈ 10⁻³⁴ makes the number large: a 100 eV photon has a frequency near 10¹⁶ Hz, not 10⁻¹⁶ Hz.
• (3) A power-of-ten slip in converting the energy: writing 100 eV as 1.6×10⁻¹⁶ J instead of 1.6×10⁻¹⁷ J gives (1.6×10⁻¹⁶)/(6.62×10⁻³⁴) = 2.417×10¹⁷ Hz.
• (4) No single slip gives 10.54×10¹⁷ Hz. Sanity check: f = E/h = (1.6×10⁻¹⁷)/(6.62×10⁻³⁴) = 2.417×10¹⁶ Hz.

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