PHYSICS 306 MODERN PHYSICS LAB

Instructor: Dr. M. Azad Islam

PHOTOELECTRIC EFFECT

Photoelectric effect refers to the phenomenon in which light shining on a material surface can transfer enough light energy to a single electron so that the electron can escape from the surface. These escaped electrons are referred to as photoelectrons. The features of the photoelectric effect cannot be explained well if it is assumed that the energy of light is distributed in a light wave. But, if it is assumed that the energy of light is distributed into small discrete packets of light energy, then all the features of the photoelectric effect can be satisfactorily explained. These discrete packets of light energy are named "photons." Their behavior is somewhat analogous to the behavior of particles. The photoelectric effect shows that light may exhibit particle like behavior in addition to the wave like behavior light exhibits in some other phenomena, such as interference.

PURPOSE: The purpose of the experiment is to investigate the particle property of the electromagnetic wave.

EQUIPMENT: Photo tube, tube mount, Source of light, a set of narrow band filters, power supply, ammeters, voltmeter and connecting wires.

THEORY: Einstein’s equation for the photoelectric effect is,

Kinetic energy of photoelectrons, K = eVs = p2/2m

hn = K + f = eVs (1)

n = eVs /h + f/ h

1/l = (e/hc)Vs + f/hc (2)

f = c/lc= 1.23 V-1/2 nm (3)

To explain the photoelectric effect it must be assumed that photons of light do exist, and that each photon has energy E = hn. The quantity "h" is a constant, called Planck’s constant, and n is the frequency of the light, which it exhibits when its wave like properties are evident. The light frequency n, wavelength l and speed c, are related by, n = c/l.

It is known that an electron requires a certain minimum energy, f to escape from a material surface. Each material has a unique value of f, typically several electron volts. (Analogously, an object requires a certain minimum energy to escape from a planet, and the escape energy for that object is uniquely different for each planet). If the photon energy (E=hn) is at least f, and the energy is transferred to one electron, the electron may leave the surface. If the photon has excess energy over f, the theory states that all the photon energy is transferred to the electron, the photo ceases to exist, and the excess energy becomes kinetic energy of the electron. The electron may keep this kinetic energy when it escapes from the surface, but will often give up some energy in random collisions as it leaves the surface. These ideas can be summarized as:

Initial electron kinetic energy = Photon energy-escape energy = hn - f

Final electron kinetic energy - losses due to random collisions during escape = Initial electron kinetic energy

There are a small number of photoelectrons with no energy loss due to collisions during escape, and for these the final kinetic energy is the same as the initial kinetic energy. Calling this Kmax and writing the above expressions for these electrons only, Kmax = hn - f

Since "h" is a constant, and f is fixed for a given surface, the maximum kinetic energy will increase as the light frequency n increases (and vice versa, until hn becomes less than f, when photoelectric emission ceases). The equation suggests a linear relationship between Kmax and n, so that if Kmax could be measured for several known values of n (i.e. with monochromatic light of known wavelength), and if the theory is correct, a graph of Kmax Vs n would be a straight line. Further, the line’s slope would be h and its y intercept would be -f, allowing these quantities to be determined and compared with accepted values.

The maximum kinetic energy of the photoelectrons can be measured with an experimental arrangement, shown below.

Light of known wavelength, selected with a suitable filter, shines on the

emitting surface. If V is zero, some of the emitted photoelectrons will hit the collecting surface and flow through the current meter, which will indicate the current flow. If V is then increased with the polarity shown, some of these photoelectrons will be decelerated on their approach to the collecting surface. In fact, some will be stopped before they reach the collector and will be returned to the emitter. Hence the current indicated will decrease. (A potential applied in this manner is often called a "retarding potential".) Any photoelectron whose kinetic energy is less eVs, where e is the electron charge, and V is the retarding potential, will be stopped and returned to the emitter. The magnitude of v is increased until the current just becomes zero. At this potential the electrons with maximum kinetic energy have been stopped, so that no electrons reach the collector. This value of v is known as the "stopping potential" or" stopping voltage" Vs. The relationship between Kmax and Vs is,

Kmax = eVs

So, if e is known, and Vs is measured, Kmax can be determined. Returning to the previous expression for Kmax and substituting the value eVs

Kmax = hn - f that is, eVs = hn - f and, Vs = (h/e)n - f/e.

If the theory is correct, then measurements of Vs and n, when graphed, should result in a straight line of slope h/e and intercept -f/e. From these h and f can be determined, compared with accepted values, and so further check the theory.

We do not have enough equipment to do these measurements in the lab. So a typical set of measurements will be given, and you are to work with these as if you had made the measurements yourself. The data is representative of that collected with a cesium-emitting surface, illuminated with filtered light from a mercury lamp.

FOR CESIUM EMITTING SURFACE AND MERCURY LAMP

4047Å violet

4358Å blue

5461Å green

5791Å yellow

Retarding Potential in Volts and Collector current in micro-amp

Volts

m Amp

Volts

m Amp

Volts

m Amp

Volts

m Amp

0.40

5.72

0.40

7.15

0.00

6.01

0.00

4.82

0.50

4.68

0.50

5.90

0.05

4.91

0.05

3.58

0.60

3.92

0.60

4.14

0.10

3.97

0.10

2.15

0.70

3.41

0.70

2.72

0.15

3.35

0.15

0.82

0.80

2.50

0.80

1.49

0.20

2.41

0.20

0.31

0.90

1.63

0.90

0.44

0.25

1.17

0.25

0.12

1.00

1.01

1.00

0.12

0.30

0.55

0.30

0.05

1.10

0.46

1.10

0.01

0.35

0.20

1.20

0.18

0.40

0.08

Plot each set of data in your lab book Photocurrent versus Voltage. Extrapolate the straight-line portion of the line and find the stopping potentials. Calculate the frequency for each set. Make a table showing wavelength, frequency and stopping potential.

Ploth Stopping potential versus frequency, and from this graph determine h and work function f. Find percent error in h and work function for cesium (f=1.95 electron volts). Read the value of the X-intercept of the graph. Explain the meaning of x-intercept.