The difference in mass of a nucleus and its constituents, $\Delta M$, is called mass defect and is given by
$\Delta M=[Z{m}_p+(A-Z)m_n]-M$

If a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass, an energy $E_b$ will be released in the process. The energy $E_b$ is called the binding energy of the nucleus.
$E_b=\Delta M{c}^2$
The ratio of the binding energy $E_b$ of a nucleus to the number of the nucleons, A, in that nucleus is called the binding energy per nucleon, $E_{bn}$.
$E_{bn}=\frac{E_b}{A}$

We have $\frac{dN}{dt}=-\lambda N$
$\frac{dN}{N}=-\lambda dt$
Integrating both sides,
${\int }_{N_0}^N\frac{dN}{N}=-\lambda {\int }_{t_0}^{t}dt$
$ln(\frac{N}{N_0})=-\lambda t$
$N=N_0{e}^{-\lambda t}$
This is the law of radioactive decay

Alpha emission: If the nucleus of a radioactive element X of mass number A and atomic number Z emits an $\alpha$ particle, a new element Y (daughter nucleus) is formed which has mass number equal to (A-4) and atomic number equal to (Z-2). Thus due to emission of an alpha particle, atomic number Z decreases by two units and mass number decreases by 4 units.
Beta emission: In emitting a beta particle the number of nucleons in the nucleus (i.e. protons and neutrons) remain same, but the number of nuetrons is decreased by one and the number of protons is increased by one.
Gamma emission: In emitting gamma particle there is no change in mass number A and atomic number Z of the nucleus.

The difference between the initial mass energy and the final mass energy of the decay products is called the Q value of the process or the disintegration energy. Thus, the Q value of an alpha decay can be expressed as
$Q=(m_x-m_y-m_{He})c^2$
This energy is shared by the daughter nucleus and the alpha particle,  in the form of kinetic energy.

A nuclear reactor is made of fuel, moderator, control rods, coolant, pressure vessel or pressure tubes, steam generator and containment.
A nuclear reactor produces and controls the release of energy from splitting the atoms of certain elements. In a nuclear power reactor, the energy released is used as heat to make steam to generate electricity.The principles for using nuclear power to produce electricity are the same for most types of reactor. The energy released from continuous fission of the atoms of the fuel is harnessed as heat in either a gas or water, and is used to produce steam. The steam is used to drive the turbines which produce electricity.

To generate useful amount of energy, nuclear fusion must occur in bulk matter. What is needed is to raise the temperature of the material until the particles have enough energy due to their thermal motions alone to penetrate the coulomb barrier. This process is called thermonuclear fusion.Thus, for thermonuclear fusion to take place, extreme conditions of temperature and pressure are required, which are available only in the interiors of stars including sun.

The fusion reaction in the sun is a multi-step process in which hydrogen is burned into helium, hydrogen being the fuel and helium the ashes. The proton-proton (p, p) cycle by which this occurs is represented by the following sets of reactions:

1. ${}_1^{1}H{+}_1^{1}H{\to }_1^{2}H+e^{+}+\nu +0.42MeV$
2. $e^{+}+e^{-}\to \gamma +\gamma +1.02MeV$
3. ${}_1^{1}H{+}_1^{2}H{\to }_2^{3}He+\gamma +5.49MeV$
4. ${}_2^{3}H{+}_2^{3}H{\to }_2^{4}He{+}_1^{1}H{+}_1^{1}H+12.86MeV$

For the fourth reaction to occur, the first three reactions must occur
twice, in which case two light helium nuclei unite to form ordinary helium
or nucleus. If we consider the combination 2(1) + 2(3) + 2(3) +(4), the net
effect is
$4_1^{1}H+2e^{-}{\to }_2^{4}He+2\nu +6\gamma +26.7MeV$