Introduction to the Project Report :
Comparing the mass of the electron with the mass of ionised hydrogen atom (proton) we see that it is lighter by a factor of 1836. This indicates that electrons are easier to accelarate than ions.
Availability of loosely bound electrons (are actually unbound) in atoms of metals is responsible for their high electrical conductivity. Within a solid piece of substance like lithium, atoms are closely packed and, therefore, the loosely bound electrons of each atom are easily moved from the influence of their nucleus to that of their neighbour. Such loosely bound electrons are called free electrons. Free electrons are held inside the metals by attractive forces at their surface and require a minimum amount of energy, called the work function of the metal, for their escape. This minimum energy can be supplied to the free electrons in the metal for their release from the metal surface by anyone of the following physical processes :
(a) Thermo ionic emission : by heating the metal sufficient thermal energy can be given to free electrons to overcome the attractive pull of the metal surface.
(b) Field emission : electrons can be extracted from metals by applying an electric field.
(c) Photoelectric emission : by shining light of high frequency (ultraviolet) on clean metal surfaces electrons from inside the metal can be released.
We shall next study the photoelectric effect. Einstein explained it on the basis of Max Planck’s Quantam idea. This laid the foundation of the Quantam theory. Therefore, the photoelectric effect is of special interest.
Hallwach discovered that an insulated zinc plate connected to a gold leaf electroscope and charged negatively losts its charge, when a beam of ultraviolet light was directed on the plate. Hallwach suggested that the metal surface loses negative charge due to ejection of electrons from its surface by the ultraviolet light. The effect was termed as Photoelectric effect. The electrons so emitted were called Photoelectrons. J.J.Thomson showed that the Photoelectrons were not different from the ordinary electrons.
Thus, the phenomenon of ejection of electrons from a metal surface, when light of sufficiently high frequency falls upon it is known as the photoelectric effect.
The phenomenon of photoelectric effect is studied by using an experimental arrangement shown in figure 1.
Monochromatic light of known frequency is focussed on the anode of an evacuated quartz tube. The anode is made out of the metal whose behaviour under exposure to light is being investigated. Flow of current in the external circuit indicates the flow of electrons emitted from the anode surface inside the tube. This is possible if the electrons are emitted with energy large enough to overcome the retarding potential between the anode and the cathode.
Explanation 1 : Free electrons in the metallic anode can absorb energy from the electromagnetic waves impinging on them. After sufficient energy has been absorbed free electrons inside the metal should be able to overcome the combined potential barrier offered by the metal surface and the retarding potential across the phototube.
Now, when the photocurrent is measured by varying (a) the intensity of light, (b) its frequency and (c) the retarding potential between the anode and the cathode, effects are observed which cannot be reconciled with the classical wave properties of light and its absorption by electrons.
Hence explanation 1 is not accepted.
The maximum kinetic energy with which the electrons leave the anode can be measured by adjusting the retarding potential till the photocurrent in the external circuit is reduced to zero. Then electrons are not able to reach the anode. If V is the cut-off voltage, the maximum kinetic energy of electrons in the phototube is eV.
When a careful study is made of photoemission by varying the above mentioned parameters in the experiment, the following important conclusions are reached :
(i) The energy distribution of the emitted electrons is independent of the intensity of the light. That is, more photoelectrons are emitted if the intensity of the light is increased but the maximum kinetic energy with which the electrons leave the metal remains unchanged. Infact, even with light of very low intensity some electrons with the same kinetic energy are emitted.
(ii) With in the limit of experimental accuracy it is observed that there is no time lag between the arrival of light at the metal and the emission of photoelectrons. The delay has been experimentally measured. The delay time has been found less than 10-9s.
(iii) For a given metal, photoelectrons are not emitted if the incident light is of frequency less than a critical value, called the threshold frequency, no matter how high its intensity.
(iv) The maximum kinetic energy with which photoelectrons are emitted from a particular metal and the frequency of the incident light are related linearly. The relation can be expressed as :
KEmax = h (n-no) ---------- (1)
As the kinetic energy of electrons cannot be negative, photoemission does not takes place when the frequency of the incident light is less than no. Although the threshold frequency no changes from metal to metal, the slope of the straight line.
eV = h (n-no), ------------ (2)
Where n is the magnitude of the cut-off voltage, is the same.
Millikan also has the credit of making the first accurate measurement of cut-off voltages for sodium metal by using monochromatic light of known frequencies. He published the graph of photocurrent versus voltage and the graph of cut-off voltage versus frequency of light. We can estimate the slope of the straight line. It is
By multiplying it with the charge of an electron, which is the fundamental charge (of an electron), e=1.602 x 10-19 C;
h = 4.124 x 1.602 x 10-15 x 10-19
= 6.6 x 10-34 Js.
The Photon :
Einstein took Planck’s idea of the quantam of energy seriously and proposed that a monochromatic electromagnetic wave of frequency consists of discrete quanta each having energy
E = hn ---- (3)
Where h is the Planck constant. The quanta of light were appropriately called photons. Each photon travels with the velocity of light. According to Einstein’s special theory of relativity energy, E and momentum, p of particles moving with the speed of light are related
E = pc ---- (4).
Where c is the speed of light.
Comparing eqs (3) and (4), the momentum of the photon is seen to be related to the wavelength of light as
Where l is the wavelength of the light.
Quantum Interpretation :
Explanation 2 : Einstein suggested that absorption of energy from a photon by a free electron inside the metal is a single event and involves transfer of energy in one lump instead of continuous absorption of energy as in the wave model of light. Energy is conserved in the process. It can be expressed by the relation.
Energy of the incident photon = maximum.
Kinetic energy of the electron + work
Function of the metal. ------ (6).
The kinetic energy of the emitted electron will be maximum if the free electron, which is released from the atom belongs to the group which has the maximum energy inside the metal. By using the Einstein relation for the energy of photons of frequency n, we can write the photoelectric emission equation, eq (6) as
Let the work function be expressed in units of frequency such that
Work function = no -------- (8)
Then the Einstein photoelectric equation, eq (7), can be re-expressed as
KEmax = h (n-no) -------- (9)
This equation is identical to the experimentally observed relationship given by eq. (1).
Hence, explanation 2 is accepted and Einstein received the Nobel Prize in physics in the year 1921 for the quantam theory of the photoelectric effect. This lead to the particle behaviour of light.
Particle Nature of Light :
Arthur Holly Compton investigated the scattering of monochromatic X-rays from electrons. He observed that the scattered X-rays had longer wavelength. The change in wavelength was found to be independent of the matter used for scattering but varies with the angle between the incident and the scattered rays. Compton could explained the effect observed by him by assigning momentum of magnitude hn/c to photons of energy hn. The elastic scattering of a photon from an electron at rest can be worked out by involving the principles of conservation of energy and conservation of momentum. The formula giving the change of wavelength of the X-ray photon is
Where j is the angle of scattering of the X-rays photon and m is the mass of electron.
The elastic process is shown diagrammatically. The recoil electrons were observed in Wilson’s cloud chamber. Wilson shared the 1927 Nobel prize in physics with Compton.
Photocell - A Technological Application :
The design of a photocell makes use of photo-emission from a metal surface for measuring the intensity of light. The photoelectrons emitted from the cathode of the photocell are drawn to the collector by an electric field. The resultant electric current is measured by a sensitive meter in the external circuit. The current obtainable from a typical photocell is of the order of a microampere.
The fundamental use of a photocell is to convert a change in the intensity of illumination into a change in electric current. This change in electric current may be used to operate controls and in light measuring devices. For example, a person approaching a door way may interrupt a light beam which is incident upon a photo cell. The abrupt change in photocurrent may be used to start a motor which opens the door or rings an alarm. Light meters in cameras work on this principle.
As we appreciated the simplicity and elegance of Einstein’s explanation of photoelectric effect we came to know about the particle behaviour of light. He introduced revolutionary ideas which were contrary to the scientific opinion of the time. The photon hypothesis disturbed the scientific community much more than the seventeenth century Newton - Huygens heated debate on the corpuscular and the wave nature of light. But the new theory gave a better description of the physical nature than the comfortable old classical ideas.
Hence, the world came to know about the dual nature of light. That is, a monochromatic beam of light of frequency , hence possessing wave attributes, manifests in some experiments as though it is a stream of quanta called photons.