In a photoelectric effect experiment, light of frequency *f* is incident on a metal surface. The provided diagram illustrates how the maximum kinetic energy *E*max of the emitted photoelectrons varies with the frequency *f* of the incident light.
(a) Explain how this diagram provides evidence for the particle nature of light and contradicts the wave model of light.
[3]
(b) Using the diagram,
(i) determine the threshold frequency *f₀* of the metal.
[1]
(ii) calculate the work function *Φ* of the metal in electronvolts. (Planck constant *h* = 6.63 × 10⁻³⁴ J s = 4.14 x 10⁻¹⁵ eV s)
[2]
(c) Light of wavelength 450 nm is incident on the metal surface. Calculate the maximum kinetic energy of the emitted photoelectrons in eV.
[2]
(d) The intensity of the 450 nm light is increased. State and explain the effect, if any, on the maximum kinetic energy of the emitted photoelectrons.
[2]
Part a
4 minutes
3 marks
Question
Explain how this diagram provides evidence for the particle nature of light and contradicts the wave model of light.
[3]
Hint Hint
Hint
Focus on two key features shown in the diagram: the threshold frequency (x-intercept) and the linear relationship between E_max and f (straight line). How do the predictions of the wave model differ for these features?
Answer Answer
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Explanation Explanation
Answer Answer
Complete Answer
Evidence for particle nature: Existence of threshold frequency (f₀) below which no emission occurs, regardless of intensity; Max KE depends linearly on frequency (E_max = hf – Φ). Contradiction of wave model: Wave model predicts emission at any frequency if intensity is high enough, and E_max should depend on intensity, not frequency.
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Part b
4 minutes
3 marks
Question
Using the diagram,
(i) determine the threshold frequency *f₀* of the metal.
[1]
(ii) calculate the work function *Φ* of the metal in electronvolts. (Planck constant *h* = 6.63 × 10⁻³⁴ J s = 4.14 x 10⁻¹⁵ eV s)
[2]
Hint Hint
Hint
(i) The threshold frequency is given by the x-intercept of the diagram. (ii) The work function is represented by the magnitude of the y-intercept, or can be calculated using Φ = hf₀ with the given value of h.
Answer Answer
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Complete Answer
(i) f₀ = 5.0 x 10¹⁴ Hz
(ii) Φ = 2.1 eV
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Part c
3 minutes
2 marks
Question
Light of wavelength 450 nm is incident on the metal surface. Calculate the maximum kinetic energy of the emitted photoelectrons in eV.
[2]
Hint Hint
Hint
First, calculate the energy of the incident photons using E = hc/λ (using h in eV s and λ converted to meters). Then apply Einstein’s equation E_max = E_photon – Φ with the work function from part (b).
Answer Answer
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Complete Answer
E_max = 0.66 eV
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Part d
3 minutes
2 marks
Question
The intensity of the 450 nm light is increased. State and explain the effect, if any, on the maximum kinetic energy of the emitted photoelectrons.
[2]
Hint Hint
Hint
Consider the particle model: What does increasing intensity correspond to? Does it change the energy of individual photons? How does this affect the equation E_max = hf – Φ?
Answer Answer
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Explanation Explanation
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Complete Answer
No effect on E_max. Increased intensity means more photons per second, but the energy of each photon (hf) remains the same. Since E_max = hf – Φ, E_max is unchanged.
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