# Unit 5 Option D The Photoelectric Effect

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## Maximum Kinetic Energy

The energy transferred from EM radiation to an electron is the energy it absorbs from one photon, hf.

The kinetic energy it will be carrying when it leaves the metal is hf minus any other energy losses.

These energy losses are the reason the electrons emitted from a metal have a range of kinetic energies.

The minimum amount of energy an electron can lose is the work function energy, so the maximum kinetic energy, Ek, is given by the equation Ek = hf - work function. Rearranging this gives you the photoelectric equation:

• hf = work function + Ek
• Ek =  1/2 x mass x velocity^2 >>> hf = work function + 1/2mv^2

The kinetic energy of the electrons is independant of the intensity, because they can only absorb one photon at a time.

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## Einstein's Photons

Einstein suggested that EM waves (and the energy that they carry) can only exist in discrete packets. He called these wave packets photons.

He saw these photons of light as having a one-to-one, particle-like interaction with an electron in a metal surface.

Each photon would transfer all its energy to one specific electron.

The photon model could be used to explain the photoelectric effect.

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## The Photoelectric Effect and Wave Theory

1. Threshold frequency:

• Wave theory says for a particular frequency of EM wave, the energy carried should be proportional to the intensity of the beam. The energy carried by the EM wave woud also be spread evenly over the wavefront.
• This means that if radiation was shone on a metal, each free electron on the surface of the metal would gain a bit of energy from each incoming wave. Gradually, each electron would gain enough energy to leave the metal.
• If the EM waves had a lower frequency (were carrying less energy) it would take longer for the electrons to gain enough energy but it would still happen eventually.
• However, electrons are never emitted unless the waves are above a threshold frequency - so wave theory can't explain the threshold frequency.

2. Kinetic energy of photoelectrons:

•  The higher the intensity of the waves, the more energy they should transfer to each electron - the kinetic energy should increase with intensity.
• Wave theory can't explain the fact that the kinetic energy depends only on the frequency in the photoelectric effect.
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## What is the Photoelectric Effect?

The Main Conclusions of the Photoelectric Effect:

1. For a given metal, no photoelectrons are emitted if the radiation has a frequency below a certain value - called the threshold frequency.

2. The photoelectrons are emitted with a variety of kinetic energies ranging from zero to some maximum value. This value of maximum kinetic energy increases with the frequency of the radiation.

3. The intensity of radiation is the amount of energy per second hitting an area of the metal. The maximum kinetic energy of the photoelectrons is unaffected by varying the intensity of radiation.

4. The number of photoelectrons emitted per second is proportional to the intensity of radiation.

5. The emission of photoelectrons is instantaneous as soon as the frequency is above the threshold frequency.

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## Stopping Potential - Part 3 - Explanation

The photoelectrons have to do work against the p.d., and so lose kinetic energy. The maximum kinetic is reduced by eV.

As p.d. across the photocell gets higher, fewer photoelectrons reach the collector electrode, so the current through the ammeter gets lower.

When the p.d. gets high enough, all the photoelectrons are stopped. This is known as the stopping potential, Vs.

No photoelectrons reach the collector electrode and the current falls to zero.

Different frequencies of light can be used, and the stopping potential for each frequency can be found.

The work done by the p.d. in stopping the fastest electrons is equal to the energy they were carrying:

• Ek = 1/2 x m x v^2 = e x V
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## Stopping Potential - Part 2 - Explanation

Stopping potential can be measured using a potential divider and a vacuum photocell. For a fixed frequency of incident light, the stopping potential can be determined.

A vacuum photocell is basically two plates within a vacuum. When connected in a circuit, a potential difference can be applied across them.

Light incident on the emitter electrode causes photoelectrons to be released. If the photoelectrons reach the collector electrode, they cause a current to flow in the circuit.

At the start the potential divider is set so that the p.d. across the photocell is zero. The ammeter records the current through the circuit caused by photoelectric emission from the photocell.

The potential divider is adjusted so the p.d. gets higher and higher (emitter electrode becoming more and more positive in relation to the collector electrode).

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