Nuclear physics

Nuclear physics

Nucleus:

Nucleus was discovered by the Rutherford and his co-workers from the α- particle scattering experiment.

The various properties of nucleus are:

a. Each nucleus has a charge. If Z is the atomic number and e is the charge of an electron, the positive charge on a nucleus is q = +Z.

b. Each nucleus has a mass. If A is the mass number M is the mass of neutron, the total mass of a nucleus is given by M = mass of proton + mass of neutron.

So, M = ZMp + (A – Z)Mn

c. Each nucleus has its own size. The radius of a nucleus of mass number A is given by:

r = roA1/3, where ro = 1.15 * 10-13cm.

d. Each nucleus possesses binding energy.

e. Each nucleus has spinning motion about its own axis in the atom due to its protons and neutrons spinning.

f. Due to spinning motion, the nuclei have magnetic moments.

The properties of nucleus are:

g. The mass of nucleus is equal to the sum of the masses of proton and neutron.

Since the size of the nucleus is very small its density is high. Nuclear density is given by

  ρ =nuclearmassnuclearvoulme$\frac{\mathrm{n}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}{\mathrm{n}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{v}\mathrm{o}\mathrm{u}\mathrm{l}\mathrm{m}\mathrm{e}}$ = AMn43πR3$\mathrm{A}\frac{{\mathrm{M}}_{\mathrm{n}}}{\frac{4}{3}\pi {\mathrm{R}}^3}$ where Mn is the mass of the nucleus A is the mass number R is the radius of the nucleus.

h. The electric quadruple moment of the nucleus describes the interaction of the nucleus with the electric field and deviation of the nucleus from the spherical symmetry.

Binding energy:

The total mass of stable nucleus is always less than the sum of the masses of its constituent by an amount ∆m called mass defect. The energy equivalent of this masses difference is referred to as the binding energy B i.e.

B=∆m C2=[{Zmp+(A-Z)mn}-m]C2

Where Z= atomic number

A=mass number

C2= velocity of light, mn=mass of neutron, mp= mass of proton and m=mass of nucleus.

Or. The energy is equal to this must be given to the nucleus to break it into itsconstituent protons and neutrons.

The average binding energy per nucleus is defined as the binding energy of a nucleus dividing by number of nucleons it contains. Figure show the binding energy per nucleon as the function of A.

Fig:

The properties of nuclear force are:

They are short ranged force.

They are strong force in nature

They have saturation properties

They are attractive force.

NUCLEAR ENERGY/NUCLEAR POWER

Fission:

The process of braking up of the nucleus of a heavy atom into two, more or less equal fragment with the releasing the large amount of energy is called fission. 

Nuclear fusion:

In this process two or lighter nuclei combination together to form a single heavy nucleus. For example when four hydrogen nuclei are fused together, the helium nucleus is formed. The mass of the single nucleus formed is always less than the sum of the masses of the individual light nuclei. The difference in mass is converted into energy a/c to Einstein’s equation

Different between nuclear fission and nuclear fusion:

Nuclear Fission	Nuclear Fusion
It is the process in which heavy (parent) nucleus split into lighter. nuclei (daughter)	It is the process in which lighter nuclei (daughter) combine to form heavy nucleus (partent)
It occurs when thermal neutrons bombard to heavy nucleus.	It occurs by heating lighter atom at high temperature.
Energy per nucleon is less than that of fusion. But energy release is greater than fusion.	Energy per nucleon is greater than that of fission. But energy released is fusion is less than that of fission.
During this process many radioactive isotopes may be formed.	During this process no radioactive isotopes are formed.
It is single stage reaction	It is multistage reaction.

Nuclei:

Isotopes are the nuclei having the same atomic number ‘Z’ but different mass no. ‘A’.

Nuclear density =mass of nucleus/ volume of nucleus

The volume of the nucleus is directly proportional to the mass no. A. if the no. of the nucleus is doubled, volume is also double. As the both mass and volume of the nucleus is increasing by the same ratio on increasing the no. of nucleus, hence the entire nucleuses have nearly the same density.

Binding energy:

the total mass of stable nucleus is always less than the sum of the masses of its constituent by an amount ∆m called mass defect. The energy equivalent of this masses difference is referred to as the binding energy B i.e.

B=∆m C2=[{Zmp+(A-Z)mn}-m]C2

Where Z= atomic number

A=mass number

C2= velocity of light, mn=mass of neutron, mp= mass of proton and m=mass of neucleus.

Or. The energy is equal to this must be given to the nucleus to break it into its constituent protons and neutrons.

The average binding energy per nucleus is defined as the binding energy of a nucleus dividing by number of nucleons it contains. Figure show the binding energy per nucleon as the function of A.

Characteristic of the curve:

1. for the lower atomic no. A, binding energy per nucleon is very low and rises as A increase and reaches a plateau of about8MeV per nucleon above A=20

2. There is maximum of about 8.8 MeV per nucleon around A=50

3. Binding energy per nucleon is almost a constant between A=20 and A=140 with the average Binding energy 8.5 MeV per nucleon.

4. Beyond at A=60 the curve decrease slowly with increasing A and reaches 7.6 MeV per nucleon at A=238. This indicates that the large nuclei are held together less tightly than that in the middle of the periodic table.

Construction and working of G – M tube or counter:

The device which is used to count the number of atoms decreasing per minute from any substance is called G – M tube or counter. With the help of this tube, we can also determine the half – life period and decay constant.

Construction:

Working:

Suppose one α – particle is decayed from radioactive substances and enters into the cylindrical tube. With increase in potential of H.T.B., α – particle accelerates and follows collision with gas atoms inside the tube. With further increase in potential of H.T.B., avalanche effect of electrons are generated by collision which results flow of current through R. Due to this potential is dropped across R. This potential drop is called pulse which amplified by amplifier and counted. Thus, one pulse represents disintegration of one atom.

Thus, by counting the number of pulse, the number of disintegration of atoms from radioactive substance can be counted for proper working of device, the voltage should be:

Or, v = v1+v22.....