Heinrich Hertz in 1887 discovered that when a beam of light of suitable high frequency strikes on a clean metal plate (such as cesium) in vacuum, electrons are ejected (or emitted) from the surface of the metal plate. This phenomenon of emission of electrons is known as Photoelectric effect. The electrons so ejected from the surface are called photoelectrons.
For example, when ultraviolet light falls on metals such as cesium (Cs), lithium (Li), sodium (Na), potassium (K), or rubidium (Rb), the photoelectric effect occurs. Cesium metal emits the electron very easily because it has the lowest ionisation energy. Therefore, it is generally used.
However, only a few metals can emit electrons when exposed to visible light. In contrast, many metals are very much capable of emitting electrons when ultraviolet light falls on them.
Since the phenomenon of the photoelectric effect occurs under the influence of light, it is called the photoelectric effect. Here, photon means light and electric means current. Thus, we can define it as:
Photoelectric effect is the phenomenon emission of electrons from the surface of a metal when the light of suitable frequency or wavelength falls upon it.
Experimental Set Up for Photoelectric Effect
The apparatus for measuring the photoelectric effect is shown in the below figure.
In the experimental setup shown above, the two electrodes are fixed through the wall of an evacuated glass tube. The cathode (i.e. negative electrode) is coated with the cesium (Cs) metal having low ionisation energy. When radiation of suitable frequency strikes on the metal (i.e. cathode), electrons are emitted from the surface of the metal.
These electrons them moves towards the positive electrons known as anode. This causes a continuous flow of electrons through the circuit, constituting in an electric current flowing through the circuit. We can measure with the help of an ammeter.
Experimental Observations
With the help of this photoelectric apparatus, some of the experimental observations are as follows:
(1) Electrons are knocked out from a metal surface only when the frequency of the incident radiation exceeds a certain frequency value. This frequency is called threshold frequency, which is denoted by ν0 . No electrons are emitted when the light has a frequency lower than a certain threshold frequency (ν0). No matter how large the intensity is? The value of ν0 depends from metal to metal depending upon its ionisation energy.
(2) The kinetic energy of emitted photoelectrons is directly proportional to the frequency of the incident radiation, but independent of its intensity. The below figure shows the variation of kinetic energy of photoelectrons with the frequency of the incident radiation.
If the frequency of the incident light is decreased below a threshold frequency, no electrons are emitted at all. The classical physics predicts that the kinetic energy of the photoelectrons should depend on the intensity of light, not on the frequency. Due to this, it fails to explain the above observations.
(3) The number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation but does not depend upon its frequency of the radiation. It means that an increase in the intensity of incident light does not increase the energy of the photoelectrons. It only increases their rate of emission.
The classical wave theory could not explain these observations according to which the energy of the light depends upon its intensity, not on the frequency.
Einstein’s Explanation of Photoelectric Effect
The classical wave theory of physics failed to explain the photoelectric effect. Albert Einstein in 1905 explained the photoelectric effect on the basis of Planck’s quantum theory. According to him, light (radiation) is made up of a stream of particles called photons. Each photon carries an energy equal to hν.
We know that electrons in metals are held by some attractive forces. To overcome these forces and release electrons, a certain minimum amount of energy is required. This energy is the characteristics of the metal and is called photoelectric work function or threshold energy which is denoted by W0.
Now, in order to release an electron from the metal surface, the photons of incident light must have equal or greater energy than the metal’s work function. We know from Planck’s quantum theory that the energy of a photon is directly proportional to the frequency of the radiation. Therefore, the incident photons must have a certain minimum frequency, called threshold or critical frequency, to overcome the work function and eject an electron.
hν0 = Photoelectric work function = threshold energy, W0
If the frequency of incident photon is less than ν0, the energy of photon will be less than the minimum energy required to eject electrons, and no electrons would be ejected. However, if the energy of the photon exceeds the minimum energy required to remove an electron, the electrons will eject from the surface of the metal.
When the light of suitable frequency (ν > ν0) falls on the surface of any active metal (such as cesium), the photon transfers its entire energy to a single electron on the surface of the metal. A part of this energy is used up in breaking the attractive force exerted by the positive ion of the metal and releasing the electron from the metal surface. The residual energy is carried by the ejected electron as kinetic energy. Since the total energy is conserved, we can write Einstein’s equation as follows:
Energy of a photon of incident radiation = Work done in escaping the electron out from the interior of the metal + K.E. of the ejected photoelectron
Mathematically, this can be expressed as:
hν = W0 + 1/2mv2
Since W0 = hν0
Hence, hν = hν0 + 1/2mv2
or, 1/2mv2 = hν – hν0 = h(ν – ν0)
Thus, Kinetic energy of ejected photoelectron = h(ν – ν0) = hc(1/λ – 1/λ0)
Since the parameters h and W0 are constant for a particular metal, so kinetic energy of ejected photoelectrons is directly proportional to frequency. Kinetic energy of photoelectrons does not depend on the intensity of light.
When the intensity of the light increases, it does not affect the energy of photons rather, it simply increases the number of photons falling on the surface of metal and hence increases the number of photoelectrons.
Solved Examples based on Photoelectric Effect
Example 1: What is the minimum energy required by photons to produce the photoelectric effect in platinum metal, given that the threshold frequency for platinum is 1.3 × 1015 sec–1 .
Solution:
The threshold frequency (ν0) is the lowest frequency that is required for photons to produce the photoelectric effect. The energy corresponding to this frequency is called minimum energy (E). Thus,
E = hν0 = 6.625 × 10-27 erg sec × 1.3 × 1015 sec-1
E = 8.6 × 10-12 erg (Ans.)
Example 2: Calculate the kinetic energy of an electron emitted from the surface of potassium metal by light of wavelength 5.5 × 10–8 cm. The work function for the given metal is 3.62 × 10–12 erg.
Solution:
Frequency ν = c/λ = 3.0 × 1010 cm sec-1 / 5.5 × 10–8 cm = 5.5 × 1017 sec-1
1/2mv2 = hν – W0 = (6.6 × 10-27 erg sec × 5.5 × 1017 ) – 3.62 × 10–12 erg
Kinetic energy = 3.63 × 10–9 erg
Thus, the electron will emit with kinetic energy of 3.63 × 10–9 erg.
FAQs on Photoelectric Effect
1. What is photoelectric effect?
The phenomenon of the emission of electrons from the surface of a metal when light of suitable frequency falls on it is called the photoelectric effect.
2. What is photoelectrons?
The electrons emitted from the surface of a metal is called photoelectrons.
3. What is threshold frequency or critical frequency?
The minimum frequency of incident light required to eject electrons from the surface of a metal in the photoelectric effect is called threshold frequency or critical frequency. It is a characteristic property of the metal.
4. What is work function or threshold energy?
The minimum amount of energy required to eject electrons from a metal surface is called work function or threshold energy. It is denoted by W0. The value of W0 depends upon the nature of the metal used for ejection of electrons. The value of work function (W0) for some metals are as:
Li = 2.42 eV
Na = 2.30 eV
K = 2.25 eV
Mg = 3.35 eV
Cu = 4.80 eV
Ag = 4.30 eV
5. What is stopping potential?
The minimum potential at which the photoelectric current becomes zero is called stopping potential. This potential is required to stop the most energetic photoelectrons from reaching the anode.
