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Nuclei

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1

Binding energy and binding energy per nucleon

If a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass, an energy will be released in the process. The energy is called the binding energy of the nucleus.

The ratio of the binding energy of a nucleus to the number of the nucleons, A, in that nucleus is called the binding energy per nucleon, .
Which of the following is wrong statement about binding energy ?
A
It is the sum of the rest mass energies of nucleons minus the rest mass energy of the nucleus
B
It is the energy released when the nucleons combine to form a nucleus
C
It is the energy required to break a given nucleus into its constituent nucleons
D
It is the sum of the kinetic energies of all the nucleons in the nucleus
In an energy emitting nuclear reaction the binding energies of reactants and products are  , respectively.Then which is  correct of the following ?
A
<
B
=
C
>
D
2

Alpha,beta and gamma particles

Alpha particleBeta particleGamma particle
It is a helium atom and contains two neutrons and two protonsIt is an electron or a positron emitted by the decay  of  nucleus It is an energetic photon or light wave.
Heavier than beta and gamma particlesMuch lighter than alpha particlesIt is a wave unlike alpha and beta particles.
Least penetrating energy. A sheet of paper or a 3-cm layer of air is sufficient to stop them.They can be stopped, for instance, by an aluminium sheet a few millimetres thick or by 3 metres of air.Highest penetrating energy.Gamma waves can be stopped by a thick or dense enough layer material, with high atomic number materials such as lead or depleted uranium being the most effective form of shielding.
Group displacement law states that the emission of or  particles results in the daughter element occupying a position, in the periodic table, either to the left or right of that of the parent element. 

Which one of the following alternatives gives the correct position of the daughter element?
A
On emission of particle - 2 groups to the right;
On emission of particle- 1 group to the right
B
On emission of particle - 2 groups to the right;
On emission of particle- 1 group to the left
C
On emission of particle - 2 groups to the left;
On emission of particle- 1 group to the left
D
On emission of particle - 2 groups to the left;
On emission of particle- 1 group to the right
In which of the following decays the atomic number decreases?
This question has multiple correct options
A
- decay
B
-decay
C
-decay
D
-decay
3

Law of radioactive decay

We have

Integrating both sides,



This is the law of radioactive decay



Answer the following question:
(i)State the law of radioactive decay. Write the SI unit of 'activity'.
(ii) There are radioactive nuclei in a given radioactive sample. If half-life of the sample is how many nuclei will decay in
4

Mean life of a radioactive substance

Mean life () = sum of life of all atom / total no of atoms present

where is the decay constant.
The activity of a freshly prepared radio-active sample is disintegrations per second, whose mean life is . The mass of an atom of this radio-isotope is kg. The mass (in mg) of the radioactive sample is
A
B
C
D
5

Half life of a radioactive substance

The half-life of a radio nuclide is the time at which both N and R have been reduced to one-half their initial values.
Putting and in the law of radioactive decay, we get:


One gram of a radioactive substance takes 50 s to lose 1 centigram. Find its half-life period
6

Change in nucleus due to alpha decay

When a nucleus undergoes alpha-decay, it transforms to a different nucleus by emitting an alpha-particle (a helium nucleus,).
For example, when undergoes alpha-decay, it transforms to

In this process, it is observed that since  contains two protons and two neutrons, the mass number and the atomic number of the daughter nucleus decreases by four and two, respectively. Thus, the transformation of a nucleus  into a nucleus can be expressed as

where  is the parent nucleus and  is the daughter nucleus.
and  - particles emitted when uranium nucleus decay to are
A
6 - particles and 2- particles
B
4 - particles and 2 particles
C
2- particles and 6 particles
D
2 -particles and 4 -particles
7

Change in nucleus due to beta decay

A nucleus that decays spontaneously by emitting an electron or a positron is said to undergo beta decay.In beta minus ( ) decay, an electron is emitted by the nucleus and a neutron transforms into a proton within the nucleus according to

In beta plus ( ) decay, a positron is emitted by the nucleus and 
a proton transforms into neutron (inside the nucleus) via

is the more stable isotope of Na than . Find out the process by which  can undergo radioactive decay.
A
emission
B
emission
C
emission
D
K electron capture
8

Calculate the energy released in a nuclear fusion reaction

Example: The ratio for deuteron and - particle are  and respectively. Find the energy released in the fusion of deuteron into -particle.

Solution:
Energy released is given as per the reaction

In the two deuterons there are total 4 nucleons and in the alpha particle there are nucleons.
Thus we get


Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron and for helium )
A
B
C
D
9

Calculate the energy released in a nuclear fission reaction

Example: In nuclear fission, % mass is converted into energy. Find the energy released in the fission of mass in .

Solution:
% mass is converted.


Let this energy is liberated per second then,
E per hour



A slow neutron strikes a nucleus of  splitting it into lighter nuclei of and  along with three neutrons. The  energy released in this reaction is :
(The masses of Uranium, Barium and Krypton in this reaction are and respectively. The mass of a neutron is )
A
B
C
D
10

Properties of nuclear force

  1. The nuclear force is much stronger than the Coulomb force acting between charges or the gravitational forces between masses. The nuclear binding force has to dominate over the Coulomb repulsive force between protons inside the nucleus. This happens only because the nuclear force is much stronger than the coulomb force. The gravitational force is much weaker than even Coulomb force.
  2. The nuclear force between two nucleons falls rapidly to zero as their distance is more than a few femtometres. This leads to saturation of forces in a medium or a large-sized nucleus, which is the reason for the constancy of the binding energy per nucleon.
  3. The nuclear force between neutron-neutron, proton-neutron and proton-proton is approximately the same. The nuclear force does not depend on the electric charge.
Write two characteristics features of nuclear force which distinguish it from Coulomb's force.