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A photosensitive surface is illuminated with the monochromatic light produced when an electron in a hydrogen atom falls from the first excited level to the ground level. If the measured stopping potential is 3.57 V, what is the threshold frequency of the material?

1. 4 × 10¹⁵ Hz
2. 5 × 10¹⁵ Hz
3. 1.6 × 10¹⁵ Hz
4. 2.5 × 10¹⁵ Hz

Correct answer: 1.6 × 10¹⁵ Hz

Solution

The n=2 -> n=1 photon has energy 13.6*(1 - 1/4) = 10.2 eV. Work function = 10.2 - 3.57 = 6.63 eV, so threshold frequency nu0 = 6.63*1.6e-19/6.63e-34 = 1.6 x 10^15 Hz.

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