Photoelectric Effect

Introduction

The photoelectric effect describes the emitation of electrons from a metal when light shines on them.

This effect was discovered in the 19th century by Alexandre Edmond Becquerel and was systematically studied by other physicists. In 1905 Albert Einstein interpreted the photoelectric effect using quantum physics.

Here are a few experiments that describe the photoelectric effect in various ways.

Experiment 1

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A glass rod is charged positively by friction, so that on the bar there is a shortage of electrons. If the bar is now held on the zinc plate, the electrons try to rebalance the charge on the bar by skipping on it. Then there is an excess of positive charge on the zinc plate which is displayed on the electrometer. Now the plate is irradiated with light from a mercury vapor lamp. No change of charge is observed since there are no electrons on the plate that could be emitted.

Experiment 2

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This time a PVC rod is charged negatively by friction, so that on the bar there is an excess of electrons. If the bar is now held on the zinc plate, the electrons try to rebalance the charge on the bar by skipping on the zinc plate. Then there is an excess of electrons on the zinc plate, which is displayed on the electrometer. Now, if the mercury lamp is turned on, it is observed on the electrometer that the charge initially decreases because the electrons are removed from the zinc plate. The charge goes briefly back to 0 and the zinc plate as such is neutrally charged. However, the light of the lamp removes more electrons, so that the plate is finally positively charged which can be seen on the electrometer again.

Experiment 3

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The same experimental set-up as in Experiment 2 with an additional Plexiglas. In contrast to Experiment 2, it is observed that no electrons are emitted.

This is because the Plexiglas filters out the high-energy UV light of the mercury vapor lamp and only the visible portion of light passes. This light does not have enough energy to release the electrons from the metal.

Work function \(W_A \)

For emitation of electrons from a metal a particular work is required, which is called the work function \(W_A \).

If a a photon has energy larger than the work function, the remaining energy is equal to the kinetic energy of the emitted electron.

$$ E_{kin} = E_{Ph} - E_A $$
(Energies of the photoelectric effect)

Work function of some metals:

Metal \( W_A \) Metal \( W_A \) Metal \( W_A \)
Aluminium 4,20 \( eV \) Calcium 3,20 \( eV \) Platinum 5,36 \( eV \)
Barium 2,52 \( eV \) Gold 4,71 \( eV \) Wolfram 4,53 \( eV \)
Cadmium 4,04 \( eV \) Iron 4,63 \( eV \) Zinc 3,95 \( eV \)
Caesium 1,94 \( eV \) Magnesium 3,70 \( eV \) Tin 4,39 \( eV \)

Planck constant

The following experiment is intended to provide a link between the frequency of the light and the kinetic energy of emitted electrons.

We use a vacuum photocell with an anode ring and a cathode of an alkali metal. Light of different frequencies falls on the cathode so that it emits electrons that move toward the anode ring. As such, a current flows.

\( U = \) -1 \(   V\)
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Increasing the reverse voltage between the cathode and anode, the electrons are decelerated by a electric field. If this field is so strong that no electron reaches the anode, the current is 0. The energy of the electric field is then equal to the kinetic energy of the electrons. The following applies:

$$ E_{kin} = E_{Feld} = U \cdot e $$

The reverse voltage and thus the kinetic energy of the electrons depends on the frequency of the light. Now one performs this experiment for some frequencies and enters the detected energy in the following \(E_{kin}(f) \) diagram.



The slope of the line is the quotient \( \Delta E : \Delta f \). It is the same for all metals and is called Planck constant.

$$ h = 6,626 \cdot 10^{-34} J \cdot s $$

On the left side the work functions \( W_A \) of the metals are shown. The equation for the line is:

$$ E_{kin} = h \cdot f - W_A $$

Comparing this with the previous formula for the energy balance of the photoelectric effect, you can see:

$$ E_{kin} = E_{Ph} - W_A $$ $$ E_{kin} = h \cdot f - W_A $$

The energy of the photons of light of frequency \( f \) is:

$$ E_{Ph} = h \cdot f $$

The intersection of the line with the x-axis is the frequency at which the photons have sufficient energy to remove electrons from the metal. This frequency is called threshold frequency and is like the work function dependant of the used metal.

$$ f_g = \dfrac{W_A}{h} $$

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