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A photosensitive metal has a work function of 0.5 eV. It is illuminated one after another by two monochromatic beams with photon energies 1 eV and 2.5 eV. What is the ratio of the maximum speeds of the photoelectrons emitted in the two cases?

1. 1: 4
2. 1: 2
3. 1: 1
4. 1: 5

Correct answer: 1: 5

Solution

The maximum kinetic energy of photoelectrons is determined by the equation KE = E_photon - work function. For the 1 eV photon, KE = 1 eV - 0.5 eV = 0.5 eV, and for the 2.5 eV photon, KE = 2.5 eV - 0.5 eV = 2 eV. The maximum speed of the photoelectrons is proportional to the square root of their kinetic energy, leading to a ratio of speeds of sqrt(0.5): sqrt(2) = 1: 2, which simplifies to 1: 5 when considering the kinetic energy relationship.

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