## Nuclei

- Get to know usually which topics are frequently asked in the NEET exam
1

## Examples of nuclear fission reactions

1. Nuclear fission of uranium to produce Barium and Krypton.

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
When a uranium isotope is bombarded with a neutron, it generates , three neutrons and :
A
B
C
D
2

We have

Integrating both sides,

This is the law of radioactive decay

% of a radioactive element disintegrates in .The percentage of the radioactive element disintegrated in will be
A
%
B
%
C
%
D
%
For a radioactive element, the correct representation of number of nuclei (N) decayed after time (t) is represented by
A
B
C
D
3

## Decay constant

If is the number of nuclei in the sample and undergo decay in time then

or
where is called the radioactive decay constant or disintegration constant.
A radioactive sample has disintegration per minute initially and disintegration per minute after seconds. Then the decay constant is
A
B
C
D
A radioactive substance after 48 days remains 25% of initial. Find disintegration constant.
A
B
C
D
none of these
4

## 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:

The rate of disintegration of a radioactive substance falls from 800 decay/min to 100 decay/min in 6 hours. The half-life of the radioactive substance is:
A
6/7 hr
B
2 hr
C
3 hr
D
1 hr
How many half-lives does Carbon-10 undergo in 2 minutes and 32 seconds? Given the half-life of Carbon-10 is about 19 seconds.
A
8 half-lives
B
7 half-lives
C
6 half-lives
D
5 half-lives
E
4 half-lives
5

## Relationship between mass and energy

By the theory of special relativity Einstein showed that mass is another form of energy and one can convert mass-energy into other forms of energy, say kinetic energy and vice-versa.Einstein gave the famous mass-energy equivalence relation

where is the speed of light.
The energy equivalent of of a substance is :
A
B
C
D
6

## 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, .
Consider the nuclear fission,
Given that the binding energy/nucleon of , and are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement:
A
8.3 MeV energy will be released
B
energy of 12.4 MeV will be supplied
C
energy of 3.6 MeV has to be supplied
D
none of the above
Consider the nuclear reaction: X A +B+ energy  .
The binding energy per nucleon for X , A , B is respectively 7.4MeV,  8.2MeV and 8.2Mev. The energy released is
A
200MeV
B
160MeV
C
110MeV
D
90MeV