The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is :

Solution

Physics sir · 4 steps

The work function stays fixed, so get it from the first reading and reuse it for the second.

1. Einstein's equation. The photon energy pays the work function first, and the rest becomes the maximum kinetic energy, which equals eV₀. In eV with hc = 1240 eV nm this reads:

   1240/(λ (nm)) = φ + V₀

2. Find the work function. For 491 nm the photon energy is 1240/491 = 2.525 eV. So φ = 2.525 - 0.710 = 1.815 eV.
3. New photon energy. With the same surface, the new photon must carry 1.815 + 1.43 = 3.245 eV. Then λ = 1240/3.245 = 382 nm.
4. So. The new wavelength is about 382 nm, which is option (d).

The idea to keep. Two stopping potentials on the same metal means one equation gives you φ and the other uses it. Use hc = 1240 eV nm so the energies and volts can be compared directly.

Answer from the NTA final answer key. Solution by PrepWiser.