THE PHOTOELECTRIC EFFECT

Contents for this page	Related topics
Introduction The photoelectric effect The photoelectric cell Failure of the wave model for light Work functions Additional questions	Transmission and scattering of light Emission and absorption spectra	Data Glossary
Learning Outcomes
After studying this section, you will (a) understand the basis for the photoelectric effect, (b) understand the reasons for the failure of the wave model for light and (c) understand Einstein's particle model for light, as well as Planck's Law.

Introduction:

Towards the end of the nineteenth century, a number of phenomena involving light were observed which could not be properly explained by the wave model, which by then had been firmly established. One such phenomenon was the photoelectric effect observed in 1887 by Hertz and further in 1888 by Hallwachs, who showed that a negatively charged zinc plate loses its charge when it is exposed to ultraviolet light, but not if exposed to white light. The experiments below demonstrate the photoelectric effect.

The photoelectric effect:

Experiment 1: Observed Effect: If an initially negatively charged zinc plate is exposed to a UV light source, the charge is lost. (Explanation)

Experiment 2: Observed Effect : If the intensity of the UV light is increased, the charge is lost more quickly. (Explanation)

Experiment 3: Observed Effect: If the zinc is initially positively charged, exposure to UV light does not lead to the discharge of the electroscope. (Explanation)

Experiment 4: Observed Effect: If visible light impinges on the negatively charged zinc plate, the electroscope is not discharged. (Explanation)

Experiment 5: Observed Effect: If the intensity of the visible light impinging on a negatively charged zinc plate is increased, we do not observe a change in the electroscope. (Explanation)

The photoelectric cell:

Further investigation of the photoelectric effect can be carried out with the photoelectric cell:

The cathode can be coated with different elements. One finds that the minimum (or threshold) frequency at which photo-electrons are emitted varies for different elements.

When light of an appropriate frequency falls on the cathode, a current is set up in an external circuit. The magnitude of the current increases as the intensity of the light having frequencies above the threshold frequency increases.

The energy of the emitted photo-electrons may be measured by setting up a potential difference between the anode and the cathode, as shown on the right.

The potentiometer enables the potential difference ac ross the cell to be varied. The current in the circuit is measured on the microammeter and the potential difference on the voltmeter.

Electrons emitted from the cathode will be repelled by the anode. The maximum energy of the emitted photoelectrons may be measured by increasing the potential difference until the current becomes zero.

Problem: Calculate the maximum energy of the electrons emitted when a caesium-coated cathode is illuminated with blue light, if the potential difference required to stop the current flow from the photo electric cell is 0.91 V. (The charge on the electron is -1x10^-19 C)

Solution: The energy W is the product of the potential difference, V, and the charge, q, on the electron:

Using this apparatus, it is found that the maximum energy of the emitted photoelectrons increases as the frequency of the incident light increases.

The failure of the wave model for light:

The wave model for light fails to account for the photoelectric effect because the energy transmitted by a wave is proportional to the amplitude. This means that if we increase the intensity of the incident radiation, photoelectrons should be emitted regardless of the frequency of the light.

As we have seen, this is not observed. The wave model cannot account for the emission of photoelectrons only after the frequency of the incident light passe s a certain threshold value.

Work functions:

Albert Einstein, extending earlier ideas of Max Planck, proposed that the energy of radiation was in discrete packets, or quanta. Each packet of light energy is called a photon.

According to Planck, the energy of the photon is proportional to the frequency of the radiation, i.e.:

where h, Planck's constant, has the value of 6.6 x 10^-34 J.s, and c is the speed of light in a vacuum, with a value of 3.0 x 10⁸ m.s^-1. When the light interacts with matter, energy is absorbed only as discrete packets and all the energy of the packet is transferred. Thus, if the energy of a photon is sufficient to excite an electron, it will do so, but if it it insufficient, it will not.

For each substance, a minimum amount of energy is required to excite a photoelectron. This is called the WORK FUNCTION, W_o, of the substance.

The kinetic energy, E_k, of the emitted electron is given by the difference in the energy of the photon of the exciting radiation and the work function:

If we increase the intensity of the incident radiation, we increase the number of photons which impinge on the substance, and this increases the number of interactions with electrons. If the photons have enough energy, this will result in the emission of an increased number of photoelectrons.

Work functions of different elements and compounds are commonly tabulated in units of ELECTRON VOLTS (eV). One electron volt is the work done in accelerating an electron across a potential difference of one volt. The equivalent energy may be calculated from

Additional questions

Experiment 1:Observed Effect: If an initially negatively charged zinc plate is exposed to a UV light source, the charge is lost.

BEFORE	AFTER

Explanation: UV light causes the release of negatively charged particles from the zinc which are repelled from the plate by its negative charge. The zinc atoms that remain are positively charged and are neutralized by combining with the negative charges.

Experiment 2: Observed Effect: If the intensity of the UV light is increased, the charge is lost more quickly.

BEFORE	AFTER

Explanation: The property of UV light that enables it to discharge the plate is proportional to the intensity of the light.

Experiment 3: Observed Effect: If the zinc is initially positively charged, exposure to UV light does not lead to the discharge of the electroscope.

BEFORE	AFTER

Explanation: Negative charges are released by the effect of UV light. These are attracted back to the positively charged zinc plate and thus no change is observed. Other experiments show that these negative charges are electrons.

Experiment 4: Observed Effect: If visible light impinges on the negatively charged zinc plate, the electroscope is not discharged.

BEFORE	AFTER

Explanation: The property of light that causes the liberation of charge is absent in visible light. We now know that it is the higher frequency of UV light that enables it to liberate photoelectrons.

Experiment 5: Observed Effect: If the intensity of the visible light impinging on a negatively charged zinc plate is increased, we do not observe a change in the electroscope.

BEFORE	AFTER

Explanation: It is not the intensity of the light that is responsible for the release of photoelectrons.

Example on work functions:

Problem: Sodium has a work function of 2.1 eV. Calculate the maximum energy of the emitted electrons when sodium is illuminated by radiation of wavelength 150 nm.
(h = 6.6 x 10^-34 J.s, e = -1.6 x 10^-19 C, c = 3.0 x 10⁸ m.s-1)

Solution: Use Planck's Equation E = hc/λ.
The energy of the incident photon is E = 6.6 x 10^-34 (J.s) x 3.0 x 10⁸(m.s^-1)/ 150 x 10⁹ (m) = 1.32 x 10^-19 J

The maximum energy is the difference between the incident energy of the photon and the work function of sodium.

Maximum energy =