Practice portal › Dual Nature of Matter and Radiation › Einstein's Photoelectric Equation and Work Function

Photons of energy 2 eV and 2.5 eV successively illuminate a metal whose work function is 0.5 eV. The ratio of the maximum speeds of the emitted electrons is ______.

Asked in GUJCET 2019 · Speed and kinetic energy of the photoelectrons

• (1) √3:2
• (2) 2:1
• (3) 1:2
• (4) 2:√3

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives 2:1. Sanity check: the kinetic energies are 1.5 eV and 2.0 eV, so the speeds are nearly equal (√3:2 ≈ 0.87), with the first one smaller.
• (3) 1:2 is the answer to the familiar version with a 1 eV photon (kinetic energies 0.5 and 2.0 eV). Here the first photon has 2 eV, giving 1.5 eV, so the ratio is √1.5:√2 = √3:2.
• (4) This is the ratio taken the other way round, v₂:v₁. The question lists the 2 eV photon first, so the ratio asked for is v₁:v₂ = √3:2.

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