Threshold frequency; photon explanation of threshold frequency.

The idea

Threshold frequency is the minimum frequency of incident electromagnetic radiation that can release electrons from the surface of a particular metal. Below it, no electrons are emitted however intense the beam or however long it shines. The photon explanation: light arrives as photons of energy E = hf, where h is the Planck constant. One photon interacts with one surface electron. If hf is below the work function ϕ, the electron cannot escape, so no emission occurs. Emission begins when hf = ϕ, giving the threshold frequency f₀ = ϕ ÷ h. Above f₀, each photon has surplus energy that becomes kinetic energy of the emitted electron. Increasing intensity increases the number of photons per second, so more electrons are released, but it does not change each photon's energy, so it cannot lower the threshold.

What earns the marks

• Threshold frequency is the minimum frequency of incident radiation that produces photoelectric emission from a given metal surface.
• Below the threshold frequency no electrons are emitted, regardless of the intensity of the radiation or the time for which it is incident.
• A photon of frequency f carries energy E = hf, where h is the Planck constant.
• Emission occurs when a single photon transfers enough energy to a single electron to overcome the work function: hf ≥ ϕ.
• The threshold condition hf₀ = ϕ rearranges to f₀ = ϕ ÷ h, so f₀ depends on the metal and not on the radiation intensity.
• Above threshold, increasing intensity increases the number of photons arriving per second and hence the number of emitted electrons per second, while the maximum kinetic energy of each electron depends on frequency.
• A correct explanation links one photon to one electron and states that a single photon must supply the whole escape energy; energy cannot be accumulated from many low-energy photons.

Common mistakes and how to put them right

• Treating threshold frequency as a property of the light source rather than of the metal surface.

  Put it right by stating that f₀ = ϕ ÷ h and so varies from metal to metal.

• Believing that very intense low-frequency light will eventually cause emission.

  Put it right by explaining that each photon still has energy below ϕ, so no single photon can release an electron.

• Saying that two low-energy photons can combine their energies to release one electron.

  Put it right by stating that in the photon model one electron absorbs one photon, so sub-threshold photons cannot cause emission.

Exam tips

• Define threshold frequency in words before using the equation f₀ = ϕ ÷ h, so the physical meaning is clear.
• When explaining why intensity does not affect threshold, compare photon energy hf with the work function ϕ rather than discussing brightness.
• Use the phrase 'one photon is absorbed by one electron' to make the quantum nature of the process explicit.