Threshold frequency

When electromagnetic radiation, like light, is incident (shone on) a metal, it can cause electrons to be emitted from the metal surface.

But this only happens with certain frequencies of light. If the frequency isn’t high enough, then no electrons will be emitted, no matter how intense the light is.

The minimum frequency of light needed to cause electrons to be emitted from a metal is called the threshold frequency.

Why is it a minimum?

• The energy needed to emit an electron from the metal is called the work function.
  • This is actually the minimum amount of energy required.
  • That’s because some electrons might be tightly bound to the metal, or deeper into it, and so they need more energy to escape.
• Because energy is directly proportional to frequency (E = hf), and because the work function is only a minimum, the threshold frequency is also a minimum.
• It’s the minimum frequency needed, because some electrons will actually require more energy (and therefore a higher frequency) to be emitted from the metal.

Calculating the threshold frequency from the work function

• We know that the energy of a photon is calculated using:
  • E = hf, where:
  • E is the energy of the photon (in joules),
  • h is Planck’s constant (6.63 \times 10^{-34} J·s),
  • f is the frequency of the photon (in hertz).
• Because the threshold frequency is just the minimum frequency needed to emit an electron, we can set the energy of the photon equal to the work function (the minimum energy needed to emit an electron) and then just solve the equation:
  • \phi=hf
  • Rearrange it to find the threshold frequency
  • f = \frac{\phi}{h}

f = \frac{\phi}{h}

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