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

Photons of energy 1 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 2015; GUJCET 2017 · Speed and kinetic energy of the photoelectrons

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

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 1:3. Sanity check: the kinetic energies are 0.5 eV and 2.0 eV (ratio 1:4), and speed goes as the square root of kinetic energy, so the speeds are 1:2.
• (3) No single slip gives 3:1, and it even puts the faster electron first. The 1 eV photon gives the smaller kinetic energy (0.5 eV against 2.0 eV), so the speeds are 1:2.
• (4) This is the ratio taken the other way round, v₂:v₁. The question lists the 1 eV photon first, and its electrons are the slower ones.

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