Maharashtra Board Class 12 Physics Chapter 14 Dual Nature of Radiation and Matter PDF Download

Dual Nature of Radiation and Matter

In earlier chapters you have studied various optical phenomena like reflection, refraction, interference, diffraction and polarization of light. Light is electromagnetic radiation and most of the phenomena mentioned have been explained considering light as a wave. We are also familiar with the wave nature of electromagnetic radiation in other regions like X-rays, gamma-rays, infrared and ultraviolet radiation and microwaves apart from the visible light. Electromagnetic radiation consists of mutually perpendicular oscillating electric and magnetic fields, both being perpendicular to the direction in which the wave and energy are travelling.

In Chapter 3 on Kinetic Theory of Gases and Radiation, you have come across spectrum of black body radiation which cannot be explained using the wave nature of radiation. Such phenomena appear during the interaction of radiation with matter and need quantum physics to explain them.

The idea of 'quantization of energy' was first proposed by Planck to explain the black body spectrum. Planck proposed a model that says (i) energy is emitted in packets and (ii) at higher frequencies, the energy of a packet is large. Planck assumed that atoms behave like tiny oscillators that emit electromagnetic radiation only in discrete packets \(E = nh\nu\), where \(\nu\) is the frequency of oscillator. The emissions occur only when the oscillator makes a jump from one quantized level of energy to another of lower energy. This model of Planck turned out to be the basis for Einstein's theory to explain the observations of experiments on photoelectric effect which we will study in the following section.

The Photoelectric Effect

Heinrich Hertz discovered photoelectric emission in 1887 while he was working on the production of electromagnetic waves by spark discharge. He noticed that when ultraviolet light is incident on a metal electrode, a high voltage spark passes across the electrodes. Actually electrons were emitted from the metal surface. The surface which emits electrons, when illuminated with appropriate radiation, is known as a photosensitive surface.

The phenomenon of emission of electrons from a metal surface, when radiation of appropriate frequency is incident on it, is known as photoelectric effect. For metals like zinc, cadmium, magnesium etc., ultraviolet radiation is necessary while for alkali metals, even visible radiation is sufficient.

Electrical energy can be obtained from light (electromagnetic radiation) in two ways (i) photo-emissive effect as described above and (ii) photo-voltaic effect, used in a solar cell. In the latter case, an electrical potential difference is generated in a semiconductor using solar energy.

Teacher's Note

When you go to a dark movie hall, the automatic door opens because of the photoelectric effect. Light hits a sensor and electrons are released, which triggers the door to open.

Exam Trick

Remember: Photoelectric effect = light knocks out electrons from metal. Just like knocking on a door, light hits the metal and electrons come out.

Points to Remember

Light is made of tiny packets called photons.
Each photon has energy equal to \(E = h\nu\).
Only certain metals release electrons when light hits them.
The type of metal matters - some need UV light, some need visible light.
Photoelectric effect is used in cameras and door sensors.

Experimental Set-up of Photoelectric Effect

A typical laboratory experimental set-up for the photoelectric effect consists of an evacuated glass tube with a quartz window containing a photosensitive metal plate - the emitter E and another metal plate - the collector C. The emitter and collector are connected to a voltage source whose voltage can be changed and to an ammeter to measure the current in the circuit. A potential difference of V, as measured by the voltmeter, is maintained between the emitter E (the cathode) and collector C (the anode), normally C being at a positive potential with respect to the emitter. This potential difference can be varied and C can even be at negative potential with respect to E. When the anode potential V is positive, it accelerates the electrons (hence called accelerating potential) while when the anode potential V is negative, it retards the flow of electrons (therefore known as retarding potential). A source S of monochromatic light (light corresponding to only one specific frequency) of sufficiently high frequency (short wavelength ≤ 10-7 m) is used.

Light is made to fall on the surface of the metal plate E and electrons are ejected from the metal through its surface. These electrons, called photoelectrons, are collected at the collector C (photoelectron are ordinary electrons, they are given this name to indicate that they are emitted due to incident light). We now know that free electrons are available in a metal plate. They are emitted if sufficient energy (we will know more about this energy later in the Chapter) is supplied to them to overcome the barrier that keeps them inside the metal.

In the late nineteenth century, these facts were not known and scientists working on photoelectric effect performed various experiments and noted down their observations. These observations are summarized below. We will try to analyze these observations and their explanation.

Observations from Experiments on Photoelectric Effect

1. When ultraviolet radiation was incident on the emitter plate, current I was recorded even if the intensity of radiation was very low. Photocurrent I was observed only if the frequency of the incident radiation was more than some threshold frequency \(\nu_0\). \(\nu_0\) was same for a given metal and was different for different metals used as the emitter. For a given frequency \(\nu\) (\(>\nu_0\)) of the incident radiation, no matter how feeble was the light meaning however small the intensity of radiation be, electrons were always emitted.

2. There was no time lag between the incidence of light and emission of electrons. The photocurrent started instantaneously (within 10-9 s) on shining the radiation even if the intensity of radiation was low. As soon as the incident radiation was stopped, the flow of current stopped.

3. Keeping the frequency \(\nu\) of the incident radiation and accelerating potential V fixed, if the intensity was increased, the photo current increased linearly with intensity as shown in Fig. 14.3.

Teacher's Note

When a student presses a button on an automatic hand dryer, the light inside detects their hand and the dryer starts. This is because of photoelectric effect working in the sensor.

Exam Trick

Remember: More light intensity = More photons = More electrons = More current. But higher intensity does NOT increase the energy of each electron.

Points to Remember

Photoelectrons are released only when light frequency is high enough.
Very weak light can still release electrons if frequency is high enough.
Stronger light releases more electrons but not faster electrons.
There is no delay between light hitting metal and electrons coming out.
Every metal has its own minimum frequency needed to release electrons.

4. The photocurrent I could also be varied by changing the potential of the collector plate. I was dependent on the accelerating potential V (potential difference between the emitter and collector) for given incident radiation (intensity and frequency were fixed). Initially the current increased with voltage but then it remained constant. This was termed as the saturation current I₀.

5. Keeping the accelerating voltage and incident frequency fixed, if the intensity of incident radiation was increased, the value of saturation current also increased proportionately, e.g., if the intensity was doubled, the saturation current was also doubled.

6. The maximum kinetic energy KE_max (and hence the maximum velocity) of the electrons depended on the potential V for a given metal used for the emitter plate and for a given frequency of the incident radiation. If the material is changed or the frequency of the incident radiation is changed, KE_max changed. It did not depend on the intensity of the incident radiation. Thus, even for very small incident intensity, if the frequency of incident radiation was larger than the threshold frequency \(\nu_0\), KE_max from a given surface was always the same for a given incident frequency.

7. If increasingly negative potentials were applied to the collector, the photocurrent decreased and for some typical value -V₀, photocurrent became zero. V₀ was termed as cut-off or stopping potential. It indicated that when the potential was retarding, the photoelectrons still had enough energy to overcome the retarding (opposing) electric field and reach the collector. Value of V₀ was same for any incident intensity as long as the incident frequency was same but was different for different emitter materials.

8. If the frequency of incident radiation was changed keeping the intensity and accelerating potential V constant, then the saturation current remained the same but the stopping potential V₀ changed. This observation is depicted in Fig. 14.5. The stopping potential V₀ varied linearly with \(\nu\) as shown in Fig. 14.6. For different metals, the slopes of such straight lines were the same but the intercepts on the frequency and stopping potential axes were different.

Teacher's Note

In old televisions, the picture tube used photoelectric effect to detect light and create images. Modern LED screens also use similar principles to detect touch on screens.

Exam Trick

Remember: Stopping potential is like the "brakes" for electrons. Higher frequency light = faster electrons = need stronger brakes (higher stopping potential).

Points to Remember

Stopping potential increases when light frequency increases.
Stopping potential does not change with light intensity.
Different metals have different stopping potentials for same light.
Saturation current happens when all released electrons reach the collector.
Increasing light intensity increases saturation current but not stopping potential.

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