The photoelectric effect: (d) work function; threshold frequency

The idea

The work function φ is the minimum energy required to remove an electron from the surface of a particular metal; it is a property of the metal and is often quoted in electronvolts, where 1 eV = 1.60 × 10⁻¹⁹ J. The threshold frequency f₀ is the lowest frequency of incident radiation that can cause photoelectric emission from that surface. It follows from Einstein’s equation with KEmax = 0, giving hf₀ = φ, so f₀ = φ/h. Radiation below f₀ cannot release electrons no matter how intense it is, because each photon then carries less than φ. The corresponding threshold wavelength is λ₀ = c/f₀ = hc/φ. Work function and threshold frequency are linked by φ = hf₀, so a larger work function means a higher threshold frequency.

What earns the marks

• The work function φ is the minimum energy needed to remove an electron from the surface of a metal.
• φ is a property of the metal surface and may be expressed in joules or electronvolts, with 1 eV = 1.60 × 10⁻¹⁹ J.
• The threshold frequency f₀ is the minimum frequency of incident radiation that produces photoelectric emission from that surface.
• At the threshold, KEmax = 0, so hf₀ = φ and therefore f₀ = φ/h.
• The corresponding threshold wavelength is λ₀ = c/f₀ = hc/φ.
• Radiation below the threshold frequency produces no emission at any intensity, because each photon carries less than the work function.

Common mistakes and how to put them right

• Confusing the work function with the threshold frequency.

  Put it right: φ is an energy in joules or electronvolts, while f₀ is a frequency in hertz, related by φ = hf₀.

• Thinking that a brighter beam below the threshold will cause emission.

  Put it right: Intensity adds more photons, but each photon still has energy below φ, so no electrons are released.

• Treating the work function as the same for all metals.

  Put it right: φ depends on the metal, so different surfaces have different threshold frequencies.

Exam tips

• Convert between joules and electronvolts carefully, using 1 eV = 1.60 × 10⁻¹⁹ J, and keep units consistent in calculations.
• Use f₀ = φ/h or λ₀ = hc/φ to move between work function, threshold frequency and threshold wavelength.
• State that below the threshold frequency no emission occurs at any intensity, and justify this using the one-photon-one-electron model.