Photoelectric Effect

What is the photoelectric effect?

When light above a certain threshold frequency hits a metal surface, electrons are emitted.

The frequency problem

• Photoelectric emission only occurs when the frequency of the incident radiation is above a certain value, the threshold frequency.

• However, according to wave theory, photoelectrons should be emitted at all frequencies.

The intensity problem

• The maximum kinetic energy of the emitted photoelectrons only depends on the frequency of the incident radiation, not the intensity

• The intensity of the incident radiation is instead proportional to the number of photoelectrons emitted per second.

Issue:

• According to wave theory, E is proportional to amplitude squared.

• So higher intensity should cause higher KE

• So increasing intensity should increase the electric field strength (EFS)

• F = e(EFS), so if EFS increases, the KE should increase.

• But this doesn’t happen.

Time delay problem

• If the incident radiation is above threshold frequency, photoelectric emission occurs without delay as soon as the incident radiation is directed at the surface

• According to wave theory, there should be a time delay before electrons are emitted. We do not observe this.

How does Einstein’s photon theory solve the intensity problem, the frequency problem and the time-delay problem?

His Solution:

• Light is made up of particles (photons)

  • E = hf

How does it help?

1. A single electron can absorb a single photon and in doing so gain energy = hf. (1-1 interaction)

2. If hf > ϕ, then electrons will be emitted. (ϕ = minimum energy required to remove electrons from the surface of the metal → work function)

3. KE_max = hf - ϕ

   KE represents left over energy. (KE electrons have from the energy left over from what was needed to remove electrons)

4. Intensity - number of photons per second per unit area. Doubling intensity will double the number of photons

How does this solve the problems?

• Intensity:

  • Doubling the intensity causes the number of photons per second to double. So, the number of electrons emitted per second doubles.

• Frequency:

  • If the frequency is less than the threshold frequency then hf < ϕ so no electrons are emitted.

• Time Delay:

  • Since the electron absorbs all the energy at once, emission is rapid.

Why do emitted photoelectrons have a range of KE’s up to a maximum value

• Electrons have varying depth within surface

• Electron-Electron interactions

• Distribution of initial energy states

What is the stopping potential?

• Electrons that escape from the metal surface can be attracted back to it by giving the surface enough positive charge. This can be achieved by connecting the positive terminal of a cell to the metal plate

• The value of the potential difference that causes the current to reduce to zero is called the stopping potential, V_s

• At this voltage, all the KE of the electron is used to do work to overcome the attraction to the positive plate.

Use V_s = (h/e) f - ϕ/e to sketch a graph and understand how this can be used to determine Planck’s constant.

The gradient would be equivalent to h/e.