Thermal Radiations

Thermal Radiations The radiations emitted by a body due to its temperature are called thermal radiations. All bodies not only emit the thermal radiations, but also absorb these radiations from surroundings. If the rate of emission of radiation is equal to the rate of absorption for a body, then the body is said to be in thermal equilibrium. The radiations emitted by a hot body depend not only on the temperature but also on the material of which the body is made, the shape and the nature of the surface.

Cavity Radiator or the Black Body

A black body or cavity radiator is that which absorbs approximately all radiations falling on it. So a black body has maximum rate of emission and absorption of radiations.
A perfect black body does not exist
Radiant Intensity
Energy emitted per unit area per unit time over all the wavelengths, is called radiant intensity. It is denoted by (RI)
Or
Power radiated per unit area over all the wavelengths is called radiant intensity.

Photo Electric Effect

The interaction between radiation and atoms of the cavity lead to the idea of quantization of energy. It means that energy can be emitted and radiated in the form of packets. Photo electric effect is another example of interaction between radiation and matter.

 Definition

When a light of suitable frequency falls on a metal surface, the electrons are emitted out. These electrons are called photo electrons and this phenomenon is called photo electric effect.

Experimental Set-up

The apparatus used to study the photo electric effect is shown in the figure. The light of a suitable frequency falls on the metal surface, which is connected to the negative terminal of variable voltage source. If the frequency is high enough, the electrons are emitted out from metal plate and accelerate towards anode. These electrons are called photo electrons and current flows through circuit due to photo electrons is called photo electric current. This phenomenon is called photo electric effect.

Maximum K.E of Photo Electrons

The maximum K.E of photo electrons can be measured by reversing the polarity of the battery. Now the photo electric current will be reduced. The photo electric current does not drop to zero immediately because the photo electrons emit from metal plate with different speeds. Some will reach the cathode even though the potential difference opposes their motion. However if we make the reversed
potential difference large enough c2
(called stopping potential) at which the
photo electric current drops to zero. This
potential difference multiplied by the
electronic charge C gives the maximum
kinetic energy of photo electrons.
Mathematically, the maximum kinetic
energy H(34 of photo electrons is
described as:

H(34 Cc2
where c2 is the stopping potential and C is the charge of an electron.

Photo Electric Effect on the Basis of Classical Wave Theory

According to classical wave theory, the light consists of electromagnetic waves and their function is to transfer energy from one place to another.
When light falls on metal surface, it transfer energy to the electrons continuously. When an electron acquires sufficient energy, it escapes out the metal surface.
This theory successfully explains the emission electrons apparently, but this theory can’t explain the three major features of photo electric effect.

·       The Intensity Problem

·       The Frequency Problem

·       Time Delay Problem

The Intensity Problem
According to classical wave theory, the light consists of scillating electric and magnetic vector, which increases in amplitude as the intensity of light beam is increased. Since the force applied to the electrons is ‘CH2’, therefore the kinetic energy of the electrons should also increased with the intensity of light. However, the experimental results suggest that the K.E of electrons is independent of intensity of light.
The Frequency Problem
According to classical wave theory, the photo electric effect should occur for any frequency of light provided that ncident light is intense enough to supply the energy needed to eject the photo electrons
Time Delay Problem
The classical wave theory predicts that there must be a time interval between the incidence of light on the metal surface and the emission of photo electrons. During this time, the electron should be absorbing energy from the beam until it has accumulated enough energy to escape the metal surface. However the experimental results show that there is no detectable time interval between the incidence of light and emission of photo electrons provided that frequency of light is equal to or greater than the threshold frequency.

Photons

In 1905, Einstein proposed quantum theory to explain the photo electric effect, according to which the light consist of bundles or packets of energy, called photons. The energy E of a single photon is

H  J d
where d is the frequency of light and J is the planks constant J  6.626 " 10%= J L s.

According to quantum theory, on photon of energy is absorbed by a single electron. If this energy is greater than or equal to a specific amount of energy (called work function), then the electrons will be ejected, otherwise not.

ENERGY FROM THE NUCLEUS

ENERGY FROM THE NUCLEUS

Nuclear Reaction Rutherford suggested in 1919 that a massive nuclear particle with sufficient kinetic energy probably be able to penetrate a nucleus. The result would be either a new nucleus with greater atomic number and mass number or a decay of the original nucleus.

Nuclear reactions are subject to several conservation laws. The classical conservation principles for charge, momentum, angular momentum, and energy (including rest energies) are obeyed in all nuclear reactions. An additional conservation law, not anticipated by classical physics, is conservation of the total number of nucleons. The numbers of protons and neutrons need not be conserved separately

Nuclear Fission

Nuclear fission is a maleficent decay procedure in which an unstable nucleus splits into two fragments of comparable mass. Fission was discovered in 1938 through the experiments of Otto Hahn and Fritz Strassman in Germany. Pursuing earlier work by Fermi, they bombarded uranium (z = 92) with neutrons. The resulting radiation did not coincide with that of any known radioactive nuclide. Urged on by their colleague Lise Meitner, they used meticulous chemical analysis to reach the astonishing but inescapable conclusion that they had found a radioactive isotope of barium.

Meituer and Otto Frisch correctly interpreted these results as showing that uranium nuclei were splitting into two massive fragments called fission fragments. Two or three free neutrons usually appear along with the fission fragments.

Both the common isotope (99.3%) 238U and the uncommon isotope (0.7%) 235U (as well as several other nuclides) can be easily split by neutron bombardment: 235U by slow neutrons (kinetic energy less than 1 eV) but 238U only by fast neutrons with a minimum of about 1 MeV of kinetic energy. Fission consequences from neutron absorption is known induced fission. Some nuclides can also undergo spontaneous fission without initial neutron absorption, but this is quite rare.

Bohr Wheeler Theory or Liquid Drop Model

According to Bohr’s liquid drop model, a nucleus can be compared with a (charged) liquid drop. Two types of forces play their role. One type of force try to keep the drop intact. They included intermolecular forces of attraction and the surface tension. Collectively they are called cohesive forces. On the other hand, there are some forces which try to de-shape the drop and to destroy its structure. they included external forces such as weight of drop. If the drop is charged, then the repulsive forces between charges on drop also try to destroy the structure of the drop. These forces are called destructive forces.

In normal liquid drop, the cohesive forces dominate destructive forces and the drop is stable. But if the charged liquid drop is of bigger size, the cohesive forces are hardly able to balance the destructive forces. And the liquid drop is in a state of highest instability and the surface oscillations will be set-up. A slight provocation may cause splitting of a drop into two or more smaller drops. Similarly, two types of forces are effective in case of a nucleus.

Strong nuclear force between the nucleon:

This is a short range force which is attractive in nature. It can be compared with the cohesive forces of the liquid drop model.

Coulomb Repulsive force between protons:

 These forces are repulsive in nature and play the role of destructive force in nucleus.

In the lighter nucleus, short range nuclear forces dominate coulomb forces of repulsion and so the nucleus is stable. But in the heavy nucleus such as +* ,-, short range nuclear forces are hardly able to balance the coulomb repulsive force. So such nucleus is in the state of highest instability

The sequence of events for a fission reaction is as follows:

1. The 235U nucleus captures a thermal (slow-moving) neutron.

2. The capture results in the formation of 236U*, and the excess energy of this nucleus causes it to undergo violent oscillations.

3. The 236U * nucleus becomes highly elongated, and the force of repulsion between protons in the two halves of the dumbbell-shaped nucleus tends to increase the distortion.

4. The nucleus splits into two fragments, emitting several neutrons in the process. This qualitative picture has been developed into a more quantitative theory to explain why some nuclei undergo fission and others don't. This explanation is given on a hypothetical potential energy function for two possible fission fragments.

If neutron absorption results in an excitation energy greater than the energy barrier height *, fission occurs immediately. Even when there isn't quite enough energy to surmount the barrier, fission can take place by quantum mechanical tunneling. In principle, many stable heavy nuclei can fission by tunneling. But the probability depends very critically on the height and width of the barrier. For most nuclei this process is so unlikely that it is never observed.

Chain Reactions

Fission of a uranium nucleus, triggered by neutron bombardment, releases other neutrons that can trigger more fissions, suggesting the possibility of a chain reaction. The chain reaction may be made to proceed slowly and in a controlled manner in a nuclear reactor or explosively in a bomb. The energy release in a nuclear chain reaction is enormous, far greater than that in any

chemical reaction. (In a sense, fire is a chemical chain reaction.) For example, when uranium is “burned” to uranium dioxide.

The heat of combustion is about 4500 J/g. Expressed as energy per atom, this is about 11 eV per atom. By contrast, fission liberates about 200 MeV per atom, nearly 20 million times as much energy.

Nuclear Fission Reactor

A nuclear reactor is a major circular system in which a nuclear chain reaction can be controlled and used to the liberate energy. In a nuclear power plant, this energy is used to generate steam, which operates a turbine and turns an electrical generator. On average, each fission of a 235U nucleus produces about 2.5 free neutrons, so 40% of the neutrons are needed to sustain a chain reaction. A 235U nucleus is much more likely to absorb a low-energy neutron (less than I eV) than one of the higher-energy neutrons (1 MeV or so) that are liberated during fission. In a nuclear reactor the higher-energy neutrons are slowed down by collisions with nuclei in the surrounding material, called the moderator, so they are much more likely to cause further fissions. In nuclear power plants, the moderator is often water, occasionally graphite. The fission rate of the reaction is controlled by inserting or withdrawing control rods made of elements (such as boron or cadmium) whose nuclei absorb neutrons without undergoing any additional reaction. The isotope 238U can also absorb neutrons, leading to 239U*, but not with high enough probability for it to sustain a chain reaction by itself. Thus uranium that is used in reactors is often "enriched" by increasing the proportion of 235U above the natural value of 0.7%, typically to 3% or so, by isotope separation processing. The most participated application of nuclear reactors is for the generation of electric power. As was noted above, the fission energy appears as kinetic energy of the fission fragments, and its immediate result is to increase the internal energy of the fuel elements and the surrounding moderator. This increase in internal energy is transferred as heat to generate steam to drive turbines, which spin the electrical generators. The energetic fission of nuclear fragments heat the water surrounding the reactor core. The steam generator is a heat exchanger that takes heat from this highly radioactive water and generates nonradioactive steam to run the turbines.

Nuclear fission reactors have many other practical uses. Among these are the production of artificial radioactive isotopes for medical and other research, production of high-intensity neutron beams for research in nuclear structure, and production of fissionable nuclides such as 239Pu from the common isotope 238U. Earlier we mentioned that an average of about 2.5 neutrons is emitted in each fission event of 235U. Meanwhile the order archive by self-sustained chain reaction, one of these neutrons must be captured by another 235U nucleus and cause it to undergo fission. A useful parameter for describing the level of reactor operation is the reproduction constant K, defined as the average number of neutrons from each fission event that will cause another event. As we have seen, K can have a maximum value of 2.5 in the fission of uranium. In practice, however, K is less than this because of several factors. A self-sustained chain reaction is achieved when K = 1. Under this condition, the reactor is said to be critical. When K is less than one, the reactor is subcritical and the reaction dies out. When K is greater than one the reactor is said to be supercritical, and a runaway reaction occurs. In a nuclear reactor used to furnish power to a utility company, it is necessary to maintain a K value close to one.