QuestionThe work function of a metal is 2.30 eV.(a) State what is meant by the work function. (1)
(b) Calculate the threshold frequency for this metal. (3)
(c) Light of frequency 4.00 × 1014 Hz is shone on the metal. Explain why no electrons are emitted, even when the light is made very bright. (2)
(d) Light of frequency 7.50 × 1014 Hz is now used. Calculate the maximum kinetic energy of the emitted electrons. (2)Answer(a) The minimum energy needed to remove an electron from the surface of the metal. (1)(b) φ = 2.30 × 1.60 × 10-19 = 3.68 × 10-19 J (1)At the threshold frequency, hf0 = φ, so:f0 = φ / h = 3.68 × 10-19 ÷ 6.63 × 10-34 = 5.55 × 1014 Hz
(2)(c) 4.00 × 1014 Hz is below the threshold frequency, so each photon has less energy than the work function. (1) Each electron absorbs the energy of one photon, and brighter light only means more photons per second, not more energetic ones, so no electron can gain enough energy to escape. (1)(d) hf = 6.63 × 10-34 × 7.50 × 1014 = 4.97 × 10-19 J½mv2max = hf − φ = 4.97 × 10-19 − 3.68 × 10-19 = 1.29 × 10-19 J
(2)Examiner tips- Always convert the work function to joules before using it with h.
- In (c), the key idea is one photon to one electron: an electron cannot build up energy from several photons.
(b) Calculate the threshold frequency for this metal. (3)
(c) Light of frequency 4.00 × 1014 Hz is shone on the metal. Explain why no electrons are emitted, even when the light is made very bright. (2)
(d) Light of frequency 7.50 × 1014 Hz is now used. Calculate the maximum kinetic energy of the emitted electrons. (2)Answer(a) The minimum energy needed to remove an electron from the surface of the metal. (1)(b) φ = 2.30 × 1.60 × 10-19 = 3.68 × 10-19 J (1)At the threshold frequency, hf0 = φ, so:
(2)(c) 4.00 × 1014 Hz is below the threshold frequency, so each photon has less energy than the work function. (1) Each electron absorbs the energy of one photon, and brighter light only means more photons per second, not more energetic ones, so no electron can gain enough energy to escape. (1)(d) hf = 6.63 × 10-34 × 7.50 × 1014 = 4.97 × 10-19 J
(2)Examiner tips- Always convert the work function to joules before using it with h.
- In (c), the key idea is one photon to one electron: an electron cannot build up energy from several photons.