Final answer:
The question asks for the threshold frequency of a metal in a photoelectric effect scenario. Einstein's photoelectric equation is used to relate kinetic energy of emitted photoelectrons to the frequency of incident light and the work function of the metal. Solving the given conditions allows calculation of the threshold frequency.
Step-by-step explanation:
The student is asking about the threshold frequency (ν0) of a metal in a photoelectric effect experiment. According to the photoelectric effect, the kinetic energy (KE) of the emitted photoelectrons is given by Einstein's photoelectric equation: KE = hν - Φ, where h is Planck's constant, ν is the frequency of the incident light, and Φ is the work function of the metal, also known as the threshold energy.
Given that one light frequency (ν1) is 3.2×1016 Hz and another (ν2) is 2.0×1016 Hz, and that the kinetic energy of photoelectrons for ν1 is twice that for ν2, we can write the following equations:
- 2(hν2 - Φ) = hν1 - Φ
- 2(h(2.0×1016 Hz) - Φ) = h(3.2×1016 Hz) - Φ
By solving these equations, we can find the threshold frequency (ν0) of the metal, which is essentially the frequency equivalent of the work function Φ: ν0 = Φ / h.