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Photo effect, photon hypothesis


The photoelectric effect, or photo effect for short, was developed by Heinrich Hertz discovered in 1887 and used by Philipp Lenard examined in more detail in 1900. We can observe this phenomenon in an experiment:

Experiment 1: A freshly (why?) Sanded zinc plate is attached to an electroscope and positively charged. Then we illuminate them one after the other with a red light and a mercury lamp. The same experiment is repeated with the negatively charged zinc plate. We can then bring a glass plate into the light path.

You can perform this experiment yourself in the following interactive animation!


What are we observing in this experiment?

The electroscope was only discharged when it was negative, using a mercury vapor lamp that emits visible and ultraviolet light. The discharge from the electroscope shows that the excess electrons are leaving the zinc plate. A glass plate in the beam path prevents the discharge. We know that glass absorbs ultraviolet light. That tells us: only UV light releases electrons from zinc.
This does not happen with a positively charged zinc plate. The UV light releases electrons from the plate, but the attraction of the positive charge brings them back.
In the experiment we also see no further discharge after the negative plate has been discharged in the UV light. The neutral plate is therefore not positively charged. Here, too, electrons are released, which means that the plate has an electron deficiency and immediately pulls it back.

When irradiated with red light, the negatively charged zinc plate was not discharged. The red light has a lower frequency than the ultraviolet. Investigations on other materials showed that only light of certain frequencies releases electrons.

The photo effect is the release of electrons by light of certain frequencies from the surface of bodies.

In a further experiment we want to investigate the influence of the intensity and the frequency of the radiation on the photo effect. The intensity I of an electromagnetic radiation is given as the quotient of the energy E in a time interval t falls on an area A, and the product of this area A and this time t defines:

(3.1)

The area A should be perpendicular to the direction of propagation of the radiation.

Experiment 2: Two metallic electrodes are attached to an evacuated vessel: a cesium cathode K (analogous to the zinc plate in the electroscope) and an anode A. The cathode is irradiated with light of different frequencies through a window made of quartz glass (also permeable to UV light). We vary the intensity of the light by moving the light source. The smaller the distance from the light source to the cathode, the greater the light intensity on the cathode! (Why? Tip: Light emits in a cone shape from the lamp.) During illumination, electrons can escape from the cesium. (For the sake of clarity, electrons are shown here as small spheres with a minus sign, as below.) When some of them reach the anode, a current flows, the strength of which we measure.

You can experiment interactively below!


How do we explain this experiment?

In contrast to zinc, electrons are already released from cesium by the low-frequency visible light. The reason for this is the smaller work function for electrons in alkali metals and cesium is one of them. (The background to this can be found in the Periodic Table of the Elements.) The minimum frequency for the release of electrons from cesium is that of yellow light.
We also observe that the current strength increases with increasing intensity. We can understand this with the wave model of light: If the light intensity is increased, according to the definition of the intensity, equation (3.1): there is more energy for the electron release per unit of time and area.
Red light does not cause any photocurrent even at high intensity (small distance to the quartz window). But this contradicts the electromagnetic wave concept of light: According to this, electrons should be set into oscillation by the periodically changing electric field strength of the light waves, so that their amplitude increases until they have enough energy to leave the metal. (The energy is proportional to the square of the amplitude.) Therefore, some time should pass before the first electrons are released. This time would then have to be shorter with stronger lighting. However, in this experiment, as in experiment 1, we noticed that the photo effect right away starts with the lighting. At high intensity ( Energy) the light of lower frequencies (the red light in the experiment) should also release electrons!
We summarize our observations:

Every substance needs its own minimum frequency of electromagnetic radiation for the electron emission: the so-called limit frequency, which does not depend on the light intensity, but only on its chemical nature.

In order to determine the kinetic energy of the released electrons, we want to measure the voltage between anode and cathode:

Experiment 3: The setup is analogous to experiment 2. Here we connect a voltmeter with a high internal resistance between the cathode and anode. The cathode is again irradiated with light of different frequencies.

Here, too, you can start the experiment yourself!


Which dependencies can we determine here?

Some of the electrons released reach the anode. The excess of electrons on the anode and their shortage on the cathode creates an electric field between them. The electrons are added to the anode until the growing field slows down the further electrons. You can therefore only reach the anode if its kinetic energy is greater than or equal to the potential energy of the electric field:

(3.2)

After the last electron is absorbed by the anode, we see that the voltage U assumes its maximum value. The last electron is also one of the fastest: one with the maximum kinetic energy. Its kinetic energy must be completely absorbed at the anode maximum potential energy to be converted:

(3.3)

Our experiment also shows that the voltage does not depend on the distance to the light source, which means:

The maximum kinetic energy of the released electrons does not depend on the light intensity.

This fact cannot be explained from the point of view of the wave theory of light. Because the greater the light intensity, the more energy should be transferred according to equation (3.1) electrons.

The maximum kinetic energy of the released electrons increases with the frequency of the incident light.

Our measurement results in the following values ​​for cesium as cathode material:

colouryellowgreenblueviolet
frequency in 1014 Hz5,195,506,887,41
Voltage UMax in V0,150,300,901,10
Energy Ekin, max= Eel, max in eV0,150,300,901,10

(1 eV is the energy that an electron receives when it passes through the voltage of 1 V.)

We wear Ekin, max against the light frequency in a diagram. All four values ​​for cesium lie on a straight line at  = 4,7  1014 Hz intersects the frequency axis. The graph for zinc also shows a straight line that is lower than the cesium straight line, but has the same slope.

Experiments with different cathode materials showed that Ekin, max from a certain, material-dependent cut-off frequency G increases linearly with the frequency of light. The intersection of the straight line with the frequency axis gives us the value of the cutoff frequency, e.g. B. G(Cs) = 4.7 1014 Hz and G(Zn) = 10.3 1014 Hz. All straight lines run parallel, their slopes are the same, i.e. independent of the material. We can calculate it using the following formula:

(3.4)

The value of this constant is Planck's quantum of action  = 4,136  10-15 eV s!
The section of the extended straight line on the energy axis is the work function W.A. = G, it is the portion of energy that is necessary for an electron to leave. The value of the work function only depends on the material.
With these considerations has Albert Einstein 1905 set up the following straight line equation for the photoelectric effect:

Einstein equation

(3.5)

According to Einstein, light energy does not appear in arbitrary amounts, but as the sum of the smallest portions. He named these portions Photons. is the energy of a photon. For A. the frequency of the light is not sufficient to release electrons from the metal. With  = 5  1014 Hz the photoelectric effect occurs with cesium, but not with zinc.

Not all electrons have maximum speed (maximum kinetic energy) when exiting the metal. Because the work to detach an electron WOj can be greater than the work function W.A. (e.g. through loss of energy in rotations). In such a case, an electron receives a correspondingly lower kinetic energy than the fastest electrons, namely: Ekin =  - WOj. The following applies:

(3.6)

At higher light intensity, it is not photons of higher energy that are emitted, but more photons at the same time, which can also release more electrons.

Even when interpreting the radiation of a black body, the assumption was made that all electromagnetic radiation has particle-like properties. When an electromagnetic oscillator of frequency Energy only as a multiple of can absorb or emit, we can imagine that this radiation consists of particles and that each of these particles has an energy wearing. A photon is therefore nothing more than a quantum of electromagnetic radiation! Originally only quanta of visible radiation were called photons. That's why photons are too Light quanta called.

In the photoelectric effect, the energy is used to detach and accelerate an electron = WOj + Ekin of a light quantum is used.

The photo effect is a further indication of the particle character of electromagnetic radiation.