1) The document reports on an experiment investigating the photoelectric effect. It describes how shining light on certain metals, like potassium, causes electrons to be ejected from the metal surface. 2) Classical electromagnetic theory could not explain observations like the instantaneous emission of electrons and the fact that kinetic energy of emitted electrons depends on frequency but not intensity of light. 3) Einstein explained the photoelectric effect using a quantum theory where light is described as discrete packets of energy called photons. When a photon strikes an electron and transfers its entire energy, the electron can escape from the metal if the photon energy exceeds the metal's work function.

1. Physics Project Report: Investigatory
Project title: “Photoelectric Effect”
Project Report on Photoelectric Effect

3. 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.

4. (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 Quantum idea. This laid the foundation of the
Quantum theory. Therefore, the photoelectric effect is of special
interest.

5. Introduction to photoelectric effect
In 1887, H.hertz performed a very interesting experiment in which
electrons (or electric current) were ejected when certain metals such as
potassium, rubidium, cesium, were exposed to a beam of light as
shown in figure
This phenomenon is called photoelectric effect.
The result obtained were:
1) The electrons are ejected from the metal surface as soon as the
beam of light strikes the surface i.e. there is no time lag between the
striking of light beam and the ejection of electrons from the metal
surface.
2) The number of electrons ejected is directly proportional to the
intensity or brightness of light.
3) For each metal, there is a characteristic minimum frequency,v0(also
known as threshold frequency) below which the effect is not observed.
At a frequency v > v0, the ejected electrons come
out with certain kinetic energy. The kinetic energy of these electrons
increase with increase of frequency of light used.

6. Theory of classical electromagnet
According to classical electromagnetic theory, this effect can be
attributed to the transfer of energy from the light to an electron in the
metal. From this perspective, an alteration in either the amplitude or
wavelength of light would induce changes in the rate of emission of
electrons from the metal. Furthermore, according to this theory, a
sufficiently dim light would be expected to show a lag time between
the initial shining of its light and the subsequent emission of an
electron. However, the experimental results did not correlate with
either of the two predictions made by this theory.
It has been observed that though number of electrons ejected depend
upon the brightness of light , the kinetic energy of the electrons does
not. For example, the red light of any brightness (intensity) may shine
on a piece of potassium metal for hours but no photoelectric are
ejected. But as soon as very weak yellow light shine on the potassium
metal , the photoelectric effect is observed.
Einstein was able to explain the photoelectric effect by using this
electromagnetic theory of radiation as a starting point.
Method of theory:
Shining a beam of light on to a metal surface can be viewed as shooting
a beam of particles, the photons. When a photon of sufficient energy
strikes an electron in the atom of the metal, it transfers its energy

7. instantaneously to the electron during the collision and the electron is
injected without any time lag or delay.
Greater the energy posed by the photon, greater will be transfer of
energy to the electron and greater the kinetic energy of the ejected
electron is proportional to the frequency of the electromagnetic
radiation.
Since the striking photon has energy equal to hv and the minimum
energy required to eject the electron is hv0 (also called work function,
w0) then the difference energy (hv-hvo) is transferred as the kinetic
energy of the photoelectron.
Following the conservation of energy principal, the kinetic energy of the
ejected electron is given by this equation given below:

8. Experimental Study
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.

9. 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,

10. 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:
K E max = h (-o) ---------- (1)
As the kinetic energy of electrons cannot be negative, photoemission
does not take 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.

11. ev = h (-o), ------------ (2)
.
Where V 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
By multiplying it with the charge of an electron, which is the
fundamental charge (of an electron), e=1.602 x 10-19 C;
We get,
h = 4.124 x 1.602 x 10-15 x 10-19
= 6.6 x 10-34 Js.
The Photon:

12. 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 = h n ---- (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
----- (5)

13. 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

14. -------- (7)
Let the work function be expressed in units of frequency such that
Work function = o -------- (8)
Then the Einstein photoelectric equation, eq (7), can be re-expressed as
K E max = h (-o) -------- (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 :

15. 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 h n. 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 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.

16. 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
A photocell can be used in any situation where beam of light falling on
it is interrupted or broken by any mean.
 To count vehicles passing a road.
 To count items running on a conveyer belt.

17.  To open doors automatically in a building such as banks or
other commercial buildings or offices.
 To operate burglar alarms.
 To produce sound in movies.
A PHOTCELL taking the incident light.

18. Conclusion
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.

19. Reference
 WWW.GOOGLE.COM
 WWW.WIKI.COM
 WWW.YAHOO.COM
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