Solar Energy
The Sun has been radiating an enormous amount of energy at the present rate for nearly 5 billion years and will continue radiating at that rate for about 5 million years more. Solar radiation reaches the Earth's upper atmosphere at a rate of 1366 watts per square meter (W/m²). While traveling through the atmosphere 6% of the incoming solar radiation is reflected and 16% is absorbed resulting in peak irradiance at the equator of 1,020 W/m². Average atmospheric conditions (clouds, dust, pollutants) further reduce insolation by 20% through reflection and 3% through absorption. Atmospheric conditions not only reduce the quantity of insolation reaching the Earth's surface but also affect the quality of insolation by diffusing incoming light and altering its spectrum.

Solar Photovoltaic Technology is employed for directly converting solar energy to electrical energy by using "solar silicon cell". The electricity generated can be utilized for different applications directly or through battery storage system. Solar Photovoltaic has found wide application in rural areas for various important activities besides rural home lighting. Remote villages deprived of grid power can be easily powered using the Solar Photovoltaic technology. The economics of rural electrification can be attractive considering the high cost of power transmission and erratic power supply in the rural areas. A typical cell develops a voltage of 0.5 - 1 V.

Nuclear Reactions

The process by which the identity of a nucleus is changed when it is bombarded by an energetic particle is called nuclear reaction. The general expression for the nuclear reaction is as follows.

Here X and a are known as reactants and Y and b are known as products. This reaction is known as (a, b) reaction and can be represented as X(a, b) Y

Q value or energy of nuclear reaction The energy absorbed or released during nuclear reaction is known as Q-value of nuclear reaction.

Q-value = (Mass of reactants – Mass of products)c² Joules

= (Mass of reactants – Mass of products) amu

If Q < 0, The nuclear reaction is known as endothermic. (the energy is absorbed in the reaction).

If Q > 0, The nuclear reaction is known as exothermic (the energy is released in the reaction).

Law of conservation in nuclear reactions

Conservation of mass number and charge number : In the following nuclear reaction

Mass number (A)→	Before the reaction	After the reaction
	4 +14 = 18	17 + 1 = 18
Charge number (Z) →	2 + 7 = 9	8 + 1 = 9

Conservation of momentum: Linear momentum/angular momentum of particles before the reaction is equal to the linear/angular momentum of the particles after the reaction, that is ∑p = 0.
Conservation of energy: Total energy before the reaction is equal to total energy after the reaction. Term Q is added to balance the total energy of the reaction.

Common nuclear reactions

The nuclear reactions lead to artificial transmutation of nuclei. Rutherford was the first to carry out artificial transmutation of nitrogen to oxygen in the year 1919.

It is called (α, p) reaction. Some other nuclear reactions are given as follows.

(p, n) reaction ⇒

(p, α) reaction ⇒

(p, γ) reaction ⇒

(n, p) reaction ⇒

(γ, n) reaction ⇒

Nuclear Fission

The process of splitting of a heavy nucleus into two lighter nuclei of comparable masses (after bombardment with a energetic particle) with liberation of energy is called nuclear fission.

The phenomenon of nuclear fission was discovered by scientist Ottohann and F. Strassman and was explained by N. Bohr and J.A. Wheeler on the basis of liquid drop model of nucleus.

Fig. 5

Fission reaction of U²³⁵

The energy released in U²³⁵ fission is about 200 MeV or 0.8 MeV per nucleon.
By fission of ₉₂U²³⁵, on an average 2.5 neutrons are liberated. These neutrons are called fast neutrons and their energy is about 2 MeV (for each). These fast neutrons can escape from the reaction so as to proceed the chain reaction they are need to slow down.
Fission of U²³⁵ occurs by slow neutrons only (of energy about 1 eV) or even by thermal neutrons (of energy about 0.025 eV).
50 kg of U²³⁵ on fission will release ≈ 4 × 10¹⁵ J of energy. This is equivalence to 20,000 tons of TNT explosion. The nuclear bomb dropped at Hiroshima had this much explosion power.
The mass of the compound nucleus must be greater than the sum of masses of fission products.
The (binding energy/A) of a compound nucleus must be less than that of the fission products.
It may be pointed out that it is not necessary that in each fission of uranium, the two fragments ₅₆Ba and ₃₆Kr are formed but they may be any stable isotopes of middle weight atoms.
Some other U²³⁵ fission reactions are:

→ Many more
The neutrons released during the fission process are called prompt neutrons.
Most of the energy released appears in the form of kinetic energy of fission fragments.

Fig. 6

Chain Reaction

In nuclear fission, three neutrons are produced along with the release of large energy (Fig. 7). Under favorable conditions, these neutrons can cause further fission of other nuclei, producing large number of neutrons. Thus, a chain of nuclear fissions is established which continues until the whole of the uranium is consumed.

Fig. 7

In the chain reaction, the number of nuclei undergoing fission increases very fast. So, the energy produced takes a tremendous magnitude very soon.

Difficulties in chain reaction

In a chain reaction, following difficulties are observed:

Absorption of neutrons by U²³⁸ The major part in natural uranium is the isotope U²³⁸ (99.3%); the isotope U²³⁵ is very little (0.7%). It is found that U²³⁸ is fissionable with fast neutrons, whereas U²³⁵is fissionable with slow neutrons. Due to the large percentage of U²³⁸there is more possibility of collision of neutrons with U²³⁸. It is found that the neutrons get slowed on coliding with U²³⁸. As a result of it further fission of U²³⁸ is not possible (because they are slow and they are absorbed by U²³⁸). This stops the chain reaction.

Removal To sustain chain reaction ₉₂U²³⁵ is separated from the ordinary uranium. Uranium so obtained ₉₂U²³⁵ is known as enriched uranium, which is fissionable with the fast and slow neutrons and hence chain reaction can be sustained.

If neutrons are slowed down by any method to an energy of about 0.3 eV, then the probability of their absorption by U²³⁸ becomes very low, while the probability of their fissioning U²³⁵ becomes high. This job is done by moderators, which reduce the speed of neutron rapidly. Graphite and heavy water are the example of moderators.

Fig. 8

Critical size The neutrons emitted during fission are very fast and they travel a large distance before being slowed down. If the size of the fissionable material is small, the neutrons emitted will escape the fissionable material before they are slowed down. Hence, chain reaction cannot be sustained.

Removal The size of the fissionable material should be larger than a critical size.

The chain reaction once started will remain steady, accelerate or retard depending upon a factor called neutron reproduction factor (k). It is defined as follows:

If k = 1, the chain reaction will be steady. The size of the fissionable material used is said to be the critical size and its mass, the critical mass.

If k > 1, the chain reaction accelerates, resulting in an explosion. The size of the material in this case is Online Classroom Program critical (atom bomb).

If k < 1, the chain reaction gradually comes to a halt. The size of the material used is said to be sub-critical.

Table 1: Types of Chain Reactions

Controlled chain reaction	Uncontrolled chain reaction
Controlled by artificial method.	No control over this type of nuclear reaction.
All neurons are absorbed except one.	More than one neutron takes part into reaction.
Its rate is slow.	Fast rate.
Reproduction factor k = 1.	Reproduction factor k > 1.
Energy liberated in this type of reaction is always less than explosive energy.	A large amount of energy is liberated in this type of reaction.
Chain reaction is the principle of nuclear reactors.	Uncontrolled chain reaction is the principle of atom bomb.

Nuclear Reactor

A nuclear reactor is a device in which nuclear fission can be carried out through a sustained and a controlled chain reaction. It is also called an atomic pile. It is thus a source of controlled energy which is utilized for many useful purposes.

Fissionable material (Fuel) The fissionable material used in the reactor is called the fuel of the reactor. Uranium isotope (U²³⁵) Thorium isotope (Th²³²) and Plutonium isotopes (Pu²³⁹, Pu²⁴⁰, and Pu²⁴¹) are the most commonly used fuels in the reactor.

Moderator Moderator is used to slow down the fast moving neutrons. Most commonly used moderators are graphite and heavy water (D₂O).

Control Material Control material is used to control the chain reaction and to maintain a stable rate of reaction. This material controls the number of neutrons available for the fission. For example, cadmium rods are inserted into the core of the reactor because they can absorb the neutrons. The neutrons available for fission are controlled by moving the cadmium rods in or out of the core of the reactor.

Coolant Coolant is a cooling material which removes the heat generated due to fission in the reactor. Commonly used coolants are water, CO₂, nitrogen, etc.

Protective shield A protective shield in the form a concrete thick wall surrounds the core of the reactor to save the persons working around the reactor from the hazardous radiations.

Uses of nuclear reactor

In electric power generation.
To produce radioactive isotopes for their use in medical science, agriculture and industry.
In manufacturing of Pu²³⁹ which is used in atom bomb.
They are used to produce neutron beam of high intensity which is used in the treatment of cancer and nuclear research.

Fig. 9

Nuclear Fusion

In nuclear fusion, two or more than two lighter nuclei combine to form a single heavy nucleus. The mass of single nucleus so formed is less than the sum of the masses of parent nuclei. This difference in mass results in the release of tremendous amount of energy.

For fusion, high pressure (≈10⁶ atm) and high temperature (of the order of 10⁷ K to 10⁸ K) is required and so the reaction is called thermonuclear reaction.
Here are three examples of energy-liberating fusion reactions, written in terms of the neutral atoms. Together the reactions make up the process called the proton-proton chain.
The proton-proton chain takes place in the interior of the sun and other stars. Each gram of the sun’s mass contains about 4.5 × 10²³ protons. If all of these protons were fused into helium, the energy released would be about 130,000 kWh. If the sun were to continue to radiate at its present rate, it would take about 75 × 10⁹ years to exhaust its supply of protons.
For the same mass of the fuel, the energy released in fusion is much larger than in fission.

Plasma The temperature of the order of 10⁸ K required for thermonuclear reactions leads to the complete ionization of the atom of light elements. The combination of base nuclei and electron cloud is called plasma. The enormous gravitational field of the sun confines the plasma in the interior of the sun.

The main problem to carry out nuclear fusion in the laboratory is to contain the plasma at a temperature of 10⁸K. No solid container can tolerate this much temperature. If this problem of containing plasma is solved, then the large quantity of deuterium present in sea water would be able to serve as in-exhaustible source of energy.

Radioactivity

The phenomenon of spontaneous emission of radiations by heavy elements is called radioactivity. The elements which shows this phenomenon are called radioactive elements.

Radioactivity was discovered by Henery Becquerel in uranium salt in the year 1896.
After the discovery of radioactivity in uranium, Piere Curie and Madame Curie discovered a new radioactive element called radium (which is 10⁶ times more radioactive than uranium)
Some examples of radio active substances are: uranium, radium, thorium, polonium, neptunium, etc.
Radioactivity of a sample cannot be controlled by any physical (pressure, temperature, electric or magnetic field) or chemical changes.
All the elements with atomic number (Z) > 82 are naturally radioactive.
The conversion of lighter elements into radioactive elements by the bombardment of fast moving particles is called artificial or induced radioactivity.
Radioactivity is a nuclear event and not atomic. Hence electronic configuration of atom don’t have any relationship with radioactivity.

Nuclear Radiations

According to Rutherford’s experiment, a sample of radioactive substance is put in a lead box and is allowed to emit radiation through a small hole only. When the radiation enters into the external electric field, it splits into three parts: α-rays, β-rays, and γ-rays.

α-decay

Nearly 90% of the 2500 known nuclides are radioactive; they are not stable but decay into other nuclides

When unstable nuclides decay into different nuclides, they usually emit alpha (α) or beta (β) particles.
Alpha emission occurs principally with nuclei that are too large to be stable. When a nucleus emits an alpha particle, its N and Z values each decrease by two and A decreases by four.
Alpha decay is possible whenever the mass of the original neutral atom is greater than the sum of the masses of the final neutral atom and the neutral helium-atom.

β-decay

There are different simple type of β-decay: β ^–, β⁺, and electron capture.

A beta minus particle (β⁺) is an electron. The emission of β ^– involves transformation of a neutron into a proton, an electron, and a third particle called an antineutrino (v).
β ^– decay usually occurs with nuclides for which the neutron to proton ratio (N/Z ratio) is too large for stability.
In β ^– decay, N decreases by one, Z increases by one and A does not change.
β ^– decay can occur whenever the neutral atomic mass of the original atom is larger than that of the final atom.
Nuclides for which N/Z is too small for stability can emit a positron, the electron’s antiparticle, which is identical to the electron but with positive charge. The basic process called beta plus β⁺ decay.

p → n + β⁺ + v (ν = neutrino)
β⁺ decay can occur whenever the neutral atomic mass of the original atom is at least two electron masses larger than that of the final atom
The mass of v and v is zero. The spin of both is 1/2 in units of h/2π. The charge on both is zero. The spin of neutrino is antiparallel to its momentum while that of antineutrino is parallel to its momentum.
There are a few nuclides for which β⁺ emission is not energetically possible but in which an orbital electron (usually in the k-shell) can combine with a proton in the nucleus to form a neutron and a neutrino. The neutron remains in the nucleus and the neutrino is emitted.

p + β⁺ → n + v

γ-decay

The energy of internal motion of a nucleus is quantized. A typical nucleus has a set of allowed energy levels, including a ground state (state of lowest energy) and several excited states. Because of the great strength of nuclear interactions, excitation energies of nuclei are typically of the order of 1 MeV, compared with a few eV for atomic energy levels. In ordinary physical and chemical transformations the nucleus always remains in its ground state. When a nucleus is placed in an excited state, either by bombardment with high-energy particles or by a radioactive transformation, it can decay to the ground state by emission of one or more photons called gamma rays or gamma-ray photons, with typical energies of 10 keV to 5 MeV. This process is called gamma (γ) decay.

All the known conservation laws are obeyed in γ-decay. The intensity of γ-decay after passing through x thickness of a material is given by I = I₀e^–μx (μ = absorption co-efficient).

Law of radioactive disintegration According to Rutherford and Soddy, law for radioactive decay is as follows: at any instant the rate of decay of radioactive atoms is proportional to the number of atoms present at that instant, i.e.,

It can be proved that N = N₀e^–λt

In terms of mass, M = M₀e^–λt, where N = number of atoms remains undecayed after time t, N₀ = number of atoms present initially (i.e., at t = 0), M = mass of radioactive nuclei at time t, M₀ = mass of radioactive nuclei at time t = 0, N₀ – N = number of disintegrated nucleus in time t, dN/dt = rate of decay, λ = decay constant or disintegration constant or radioactivity constant or Rutherford Soddy’s constant or the probability of decay per unit time of a nucleus.

Activity It is defined as the rate of disintegration (or count rate) of the substance (or the number of atoms of any material decaying per second), i.e.,

where A₀ = activity of t = 0 and A = activity after time t.

Comment

Units of activity (radioactivity)

The units of radioactivity are Becqueral (Bq), Curie (Ci) and Rutherford (Rd).

1 Becquerel = 1 disintegration/s,

1 Rutherford = 10⁶ dis/s, 1 Curie = 3.7 × 10¹¹ dis/s

Half life (T_1/2) Time interval in which the mass of a radioactive substance or the number of it’s atom reduces to half of it’s initial value is called the half life of the substance, i.e., if N = N₀/2, then t = T_1/2.

Fig. 10

Hence, from

Mean (or average) life (τ) The time for which a radioactive material remains active is defined as mean (average) life of that material.

It is defined as the sum of lives of all atoms divided by the total number of atoms, i.e.,

Fig. 11

From = slope of the line shown in the graph, i.e., the magnitude of inverse of slope of curve is known as mean life (τ).
From N = N₀e^–λt, if t = 1/λ = τ

⇒ of N₀.

i.e., mean life is the time interval in which number of undecayed atoms (N) becomes 1/e times or 0.37 times or 37% of original number of atoms.

or
It is the time in which number of decayed atoms (N₀ – N) becomes (1 – 1/e) times or 0.63 times or 63% of original number of atoms.
From

i.e., mean life is about 44% more than that of half life, which gives us τ > T_(1/2).