NUCLEUS

The central core of the atom which contains all the positive charge and most of its mass.It consists of

Property Protons Neutrons

Nature of Charge Positive Neutral

Value of charge + 1.6 1019 C 0

Mass 1.6726 1027 kg = 1.007825

a.m.u

1.6750 1027 kg = 1.008665

a.m.u.

These two constituents of a nucleus (protons and neutrons) are called nucleons.

!! Hydrogen nucleus consists of a single proton alone, the nuclei of other elements consist of both neutrons

and protons. The different types of nuclei are often called nuclides.

Note. Since neutron is a neutral particle, it has high penetrating power and very low ionising power.

Further, electric and magnetic fields have no affect on it.

ATOMIC NUMBER AND MASS NUMBER

(i) Atomic number (Z): The number of protons in a nucleus is called the atomic number.

In a neutral atom, the number of electrons is equal to the atomic number Z.

(ii) Mass number (A): The total number of nucleons (protons plus neutrons) is called mass number. This

name is used since the mass of a nucleus is very closely A times the mass of one nucleon.

Clearly, neutron number, N = A Z

Nuclear notation (Nuclide) : To specify a given nucleus, we need give only A and Z. A nucleus is

represented by a special symbol which takes the form: z X A

Here X is the chemical symbol for the element.

PROPERTIES OF ATOMIC NUCLEUS

(i) Size of nucleus: Radius R of the nucleus is given by;

3/1

0 ARR here, Ro =1.2 x 10 15 m

(ii) Nuclear density:

EINSTEIN'S MASS-ENERGY RELATION

Mass and energy are interconvertible. E = m c2

where c = velocity of light ( = 3 108 ms1)

ISOTOPES ISOBARS ISOTONES

The nuclei that have the same

number of protons (Z) but

different number of neutrons

(different A) are called isotopes.

The atoms of different elements

which have the same mass

number A but differ in their

atomic number Z are called

isobars.

The nuclei of isobars have

different number of protons (Z)

and different number of neutrons

(A Z).

The nuclides which contain the

same number of neutrons are

called isotones.

6C11, 6C

12, 6C13, 6C14, 6C

15 and 6C16

are isotopes of carbon

11Na23 and 12Mg

23 are the isobars.

15P31 and 16S

32 are the isotones

because the nuclides of both

contain the same (i.e. 16)

neutrons.

NUCLEAR FORCE

The strong forces of attraction which firmly hold the nucleons in

the nucleus are known as nuclear forces.

Properties of nuclear forces:

(i) They are charge independent i.e. they are the same between p

and n or between p and p or between n and n.

(ii) They are short-range forces upto 10-15m.

(iv) They have saturation character i.e. they abruptly become zero

as the inter-nucleon distance is increased to a certain value (about 1014 m). Therefore, nuclear forces do not

increase with the increase in the number of nucleons.

(v) They are strongest i.e. their magnitude is so high that a huge energy is required to divide a nucleus into

its constituents.

MASS DEFECT

The difference between the actual mass of the nucleus and the sum of masses of the constituent nucleons is

called mass defect i.e

Mass defect, m =[zMp + (AZ) Mn ] M where M = actual mass of the nucleus and A = mass number

NUCLEAR BINDING ENERGY

It is the energy with which the nucleons are held together within the nucleus.

It is measured by the total energy required to liberate all the nucleons from the nucleus (i.e. to

disintegrate the nucleus completely into its constituent particles) .

Eb = 2

!! m should be in kg. If it is in amu then use 1 amu = 931.5MeV

ORIGIN

A nucleus is formed by coming together of the constituent nucleons. It has been observed experimentally

that the mass of the nucleus is always less than the sum of the masses of its constituent nucleons. This

energy liberated contribute the decrease in mass (mass defect)

BINDING ENERGY PER NUCLEON

Ebn = Eb / A=2/A

Greater the binding energy per nucleon, the greater is the stability of the nucleus

BINDING ENERGY CURVE

In heavy nuclei number of proton is

large therefore due to large repulsion

binding energy decreases.

Following are the characteristics of

the curve:

(i) The curve rises as A (mass number)

increases and reaches a value of about 8

MeV per nucleon above A ~ 15.

(ii) The nuclei with A ~ 60 have the

greatest binding energy per nucleon and

are also the most stable nuclei.

(iii) The very small and very large nuclei have less binding energy per nucleon indicating that these nuclei

are held less tightly than those in the middle of the periodic table.

(iv) Except for a few light nuclei, the average binding energy per nucleon is about the same (i.e. about 8

MeV) for all nuclei. This proves the saturation character of the nuclear forces.

(v) The binding energy curve is used to analyze nuclear processes such as fission and fusion

(a) For fission:

From curve it is clear that B.E. / nucleon for a heavy nucleus is lower therefore it is unstable but when it

breaks down , then it forms two medium weight nuclei (lie in the middle portion on curve) which have

more B.E. / nucleon than heavy one and hence more stable .Therefore energy released in this process.

(b)For fusion:

From curve it is clear that B.E. / nucleon for lighter nuclei is lower therefore they are unstable but when

they fused together , then they forms a heavy nucleus (lie in the middle portion on curve) which has more

B.E. / nucleon than lighter ones and hence more stable. Therefore energy released in this process.

FACTORS UPON WHICH STABILITY OF A NUCLEUS DEPENDS

(i) In general, the greater the value of binding energy per nucleon, the greater is the stability of the nucleus.

(ii) Nuclei having n/p ~ 1 but not less than one.

NATURAL RADIOACTIVITY

The process of spontaneous disintegration of the nuclei of heavy elements with the emission of certain

types of radiations is known as natural radioactivity.

The elements whose nuclei spontaneously disintegrate are called radioactive elements e.g. uranium (Z =

92), radium (Z = 86) etc.

LAWS OF RADIOACTIVE DECAY

The rate of disintegration at any time (i.e. number of atoms that disintegrate per second) is directly

proportional to the number of radioactive atoms present in the sample at that time. This is known as decay

law.

Let at time t = 0 number of atoms in radioactive element is

number after time t the no. of atoms remain N due to decay. Further after time dt the number of atom dt

disintegrate.

Then at time t rate of disintegration will be dN/dt. From decay law

Ndt

dNN

dt

dN - - - - - - - (1)

Here is radioactive constant. It is also known as decay constant or disintegration constant.

The ve sign indicates that as time increases the value of N decreases.

dtN

dN

Integrating both side of equation.

dtNN

dN tN

No

0

t

NNe dttNLog o

0

tN

NetNLog

o0

)0(0 tNLogNLog ee tN

NLog e

0

- - - (2)

Taking antilog on both the sides

t

eN

N

0 t

eNN

0 - - - - - (4)

This eq shows that number of radioactive atom decreases exponentially with time. This means that the

number of radioactive atom decreases rapidly at first and then more and more slowly as time goes on. This

is shown in graph.

Decay constant

Puting t=1/ in eq (4) (i.e = 1/t)

tteNN

1

0

10

eNN

00 37.0 N

e

NN

Hence decay constant may be defined as the reciprocal of time during which the no. of atoms of a

radioactive substance falls to 1/e or 37% of original number of atoms presents (No).

Half life(T1/2): - Time in which the radioactive atoms are reduced to half of there initial amount.

From exponential law of disintegration eq (4) N = No et

When time t =T , then N=No/2, putting this value in equation.

21

20

0

T

e

TeN

N

eT = 2

Taking log on both the sides

loge eT = loge 2 T loge e = loge2 T = loge2

So half-life period

693.02log TT e

Average life or Mean Life: - The mean life or average life of a radioactive substance is defined as the ratio

of total life time of all the radioactive atoms to the total no of such atoms in it. Average life period

1

atoms of number Total

atoms all of periods life the of sum Ta

The average life and half-life of a radioactive element s are different elements and it is not possible to

change it.

Notes:

(i) For the decay to take place, the mass of the parent nucleus must be greater than the total mass of the

decay products. In other words, radioactive decay is possible only if

m (parent) > [m (daughter ) + m (decay particle)]

If the decay products have more mass than the parent nucleus, then additional energy is required from

external source to accomplish the decay.

(ii) The difference between the initial and final mass energies is called the Q value of the reaction.

Using E = m c2, we have, Q = [ m (parent) m (daughter) m (decay particle )] c2

If Q is positive, spontaneous decay may occur but if Q is negative, then spontaneous decay cannot occur.

The positive Q value is available to the decay products as kinetic energy.

Activity: Rate of disintegration of a radioactive material.

A=N

Unit: Becquerel(Bq) = one disintegration per second.

ALPHA DECAY

The phenomenon of emission of -particle from a radioactive nucleus .

(i) Occurs when no. of p > no. of n (since repulsive force increases)

(ii) In this process n /p ratio increases.

e.g. 92U238 90U

234 + 2He4 + Q

GAMMA DECAY

The phenomenon of emission of gamma ray photon

from a radioactive substance.

(i) After the emission of alpha or beta particle when an

excited radioactive nucleus make transition to lower

energy state then it emits gamma radiations. (to attain

stability)

(ii) Energy of gamma ray is order of MeV because

difference in energy levels in a nucleus is of order of MeV.

BETA DECAY

The phenomenon of emission of an electron or positron from a radioactive substance.

(i) Occurs when no. of p < no. of n

(ii) In this process n /p ratio decreases.

e.g. - 15P32 16S

32 + -1e0 +

+decay , 11Na22 10Ne

22 + 1e0 +

Mechanism

In -decay, a neutron is transformed into a proton within nucleus with an antineutrino.

n p + + -1e0 +

p n + + 1e0 +

!! K.E. of beta particle is continuous because energy is shared by antineutrino.

NUCLEAR REACTION

Transformation of a stable nucleus into another by bombarding the former with suitable high energy

particle.

First successful nuclear reaction was carried out by Rutherford.

7N14 + 2He

4 8O17 + 1H

1 or N(

NUCLEAR FISSION

The splitting of a heavy nucleus (A > 230) into two nuclei of comparable masses when it is bombarded

with a neutron of suitable energy with the release of large amount of energy.

92U235 + 0n

1 56Ba144 + 36Kr

89 + 3 0n1 + 200 MeV

CHAIN REACTION

A nuclear reaction in which the particle which start the reaction is also produced during the reaction

to carry on the reaction further and further.

e.g. fission of U-235.

Neutron multiplication factor (or reproduction factor)

k = Rate of production of neutrons

Rate of loss of neutrons

(i) If k > 1. Size of material is super critical. Results in explosion.

(ii) If k < 1. Size of material is sub critical. Reaction gradually comes to halt.

(iii) If k = 1.Reaction will be steady or sustained. Size of material is critical and mass is critical mass.

TYPES OF CHAIN REACTIONS

1. Explosive chain reaction: A nuclear chain reaction in which fission neutrons keep on increasing till the

whole of the fissionable material is consumed (or disintegrated) is known as explosive chain reaction.

Such a reaction proceeds very quickly with the liberation of huge amount of energy in an extremely short

time. Therefore, it is accompanied by an explosion.e.g. An atom bomb

2. Controlled chain reaction. A chain reaction that proceeds slowly without any explosion and in which

energy released can be controlled is known as controlled chain reaction.e.g. In nuclear reactor

NUCLEAR REACTOR

A nuclear reactor is a

device in which controlled

fission chain reaction takes

place.

Principle. Controlled

fission chain reaction of U-

235. The enormous heat

produced in the fission

process is used to convert

water into steam at high

pressure. The steam passes

over the blades of a turbine

and causes it to rotate. An electric generator coupled to the turbine produces electricity.

Construction:

(i) Nuclear fuel: The nuclear fuel is sealed in long, narrow metal aluminium tubes called fuel rods. The

enriched U-235 ensures that at least one of the neutrons produced by a fission reaction has a good chance of

causing fission in another U-235 nucleus.

(ii) Moderator: The neutrons released by fission normally move very fast (2 MeV). At this high speed, the

chance of a neutron being captured by another U-235 nucleus is very small. If the neutron is slowed, its

chance of capture is much better. The slow neutrons are called thermal neutrons and possess energy of

the order of 0.0235 eV. In order to slow down the fast fission neutrons, a moderator is used.

e.g. graphite and heavy water.

!!Heavy water is preferred

(i) It does not absorb neutron (ii) It is more effective because mass of hydrogen atom is comparable to

mass of neutron therefore neutron suffer elastic collision and can be slowed down effectively.

(iii) Control rods: The control rods keep the net rate of production of neutrons to the required level by

capturing the necessary proportion of neutrons before they initiate fission. When the control rods are

moved upward out of the reactor, the number of neutrons left to produce fission is increased. On the other

hand, when the control rods are lowered, the number of neutrons for producing fission is decreased.

e.g. Cadmium or Boron

Safety rods: To stop the fission immediately when required.

(iv) Coolant: To remove heat from the reactor core and take it to the place of its utilisation e.g. steam

turbine. The steam runs the steam turbine coupled to the generator.

e.g. Liquid sodium and heavy water

(v) Protective shield: In a nuclear reactor, many types of harmful radiations are emitted. In order to

prevent these radiations from reaching the persons working near the reactor, the reactor is enclosed in thick

concrete walls.

Working: Heat energy produced by fission is taken out with the help of coolant and utilize to produce

steam.This steam rotates the turbine attached to generator to producd electricity.Spent steam is condensed

and can be used again and again.

Uses:

(i)To generate electric power, (ii)to produce radioactive isotopes for their use in medical science,

agriculture and industry, (iii) To produce high-velocity beams of neutrons for their use in nuclear physics.

NUCLEAR FUSION

The process of combining two light nuclei to form a heavy nucleus with the release of huge amount of

energy is known as nuclear fusion.

HOW TO CAUSE FUSION?

Very high temperature (108K) and Very high pressure.

As high temperature is required to cause fusion therefore it also called thermo-nuclear reaction.

SOURCE OF SUN/STAR/STELLAR ENERGY

Fusion reactions in the sun are responsible for its enormous heat. These reaction takes place in the core of

the sun where high temperature and pressure is available.

Proton-proton cycle

In this reaction, two protons fuse to make a deuteron and finally helium through the following intermediate

reactions:

2 1H1 + 2 1H

1 2 1H2 + 2+1e

0 + energy ...(i)

2 1H2 + 2 1H

1 2 2He3 + energy ...(ii)

2He3 + 2He

3 2He4 + 2 1H

1 + energy ...(iii)

Summing up all the three above equations and canceling out the nuclides which occur on both sides,

we get,

4 1H1 2He

4 + 2 +1e0 + energy

COMPARISON BETWEEN FISSION AND FUSION

S.No. Fission Fusion

1 Splitting of heavy nucleus combining of light nuclei

2 can be controlled can not be controlled

3 emit harmful radiations no harmful radiations

4 less energy than fusion more energy than fission

Conversion of U-238 into Pu-239

92U238

+n 92U239 93Np

239 + e- +

93Np239 94Pu

239 + e- +

!! Ionising power of alpha particle more is because it has more mass and charge.

!! Neutron is an unstable particle.

!! Alpha particles are easily absorbed ,highest Ionising power,deflected by magnetic and elcteric field

; beta particles similar to cathode rays, deflected by magnetic and elcteric field; gamma rays similar

to X rays ,travel with greatest speed,not deflected.

Atomic Nucleus

01. Show that nuclear density is constant.

02. Find an expression for concentration of radioactive atom at any time t, N = N0e-t.

03. Plot a graph between the Binding energy per nucleon and mass number. And hence explain from the

graph why some atom undergo fission & some undergo fusion. Write two inferences from the graph.

04. Draw a graph showing the variation of Nuclear force/potential energy of nucleons with distance. Mark

the attractive and repulsive region.Write its four properties.

05. What is a nuclear reactor. Explain its construction & working with a well labeled diagram.

06. What is radioactivity. Why certain heavy atoms show the phenomenon of radioactivity.

07. What happens to n / p ratio when

(i) - Particle is emitted (ii) -, + Particle is emitted (iii) - ray is emitted Explain with example.

08. Define activity. Write its unit.

09. Why energy spectrum of - particle is continuous. Draw the distribution of kinetic energy of emitted electron emitted in the decay of 60Co nucleus.

10. Draw the energy level diagram showing the emission of - rays by a 60Co nucleus subsequent to beta decay.

11. How will you convert 23892U into 239

94PU.

12. Write the requirement for controlled thermonuclear reaction.

13. Name the source of stellar energy & hence define nuclear fusion. Write one reaction for it.

14. Compare the radius of two nuclei with mass number 1 and 27.

15. Why heavy water is used to slow down fast moving neutrons.

16. Define half life period & decay constant of a radioactive substance. Establish a relation between

them.

17. Define "disintegration constant " & "meanlife" of a radio active substance. Give the unit for each.

18. which is more stable 73X or 4

3Y. Why ?Are they isotope of the same element.

19. Find the mass number and atomic number for each

D D1

D2 D3

D4 (if for D2 Z = 71, A =176)

20. A neutron is absorbed by a 63Li nucleus with subsequent emission of an alpha particle. Write the

corresponding nuclear reaction.

21. 23892U decays successively to form 234

90Th, 234

91Pa, 234

92U, 230

90Th , 226

88Ra & 226

86Rn. What are the

radioactive radiation emitted in each decay process.

22. Which of the following radiations -rays, -rays, -rays are (i) Similar to x-rays (ii) easily absorbed by matter (iii) travel with greatest speed

(iv) similar to cathode rays

23. Write the equation for & + decay within a nucleus. 24. Define mass defect and binding energy.

Numericals

01. The half life period of a radio active substance is 30 days. What is the time taken for 3/4th of its

original mass to disintegrate. Calculate the decay constant.

02. The half life of a radioactive substance is 1.192 x 107 s against alpha decay. Calculate the decay rate

for 3.18 x 1015 atoms of the substance.

03. Find the half life period of a radio active material if its activity drops to 1/16th of its initial value in 30

days. Also find the mean life or average life of the sample and also the disintegration constant.

04. Calculate B. E/ nucleon of Bi209. Given m(83Bi209 ) = 208.980388 amu , mn = 1.008665 amu & mp =

1.007825 amu , 1 amu = 931.5 MeV.

05. A neutron is absorbed by nucleus by the subsequent emission of alpha. Calculate the energy

released in the following nuclear reaction. Write the corresponding nuclear reaction.Calculate the

energy released.

36Li = 6.015126u , 0

1n = 1.008665 u, 24He = 4.002604u, 1

3H = 3.016049u

06. The isotopes of chlorine 35Cl & 37Cl have abundance 75.4 % & 24.6 % respectively. If there

masses are 34.98 U & 36.98 U, then what is the mass of natural chlorine atom. (35.47u)

07. The half life of 92238U against -decays is 4.5 x 109 year. What is the activity of 1g sample of 92

238U .

(1.23 x104Bq)

08. Tritium has a half-life of 12.5y against beta decay. What fraction of a sample of pure tritium will

remains undecayed after 25y.

09. Given 92238U = 238.050790u, 11H = 1.00783u, 91

237Pa = 237.05121u. Show that 92238U cannot

spontaneously emit a proton.

10. How long an electric lamp of 100W can be kept glowing by fusion of 2kg of Deuterium. The fusion

reaction can be taken as

12

12

23

01 32H H He n MeV . (4.9 x104 s)

11. Two nuclei P,Q have equal number of atoms at t=0. Their half lives are 3 hours and 9 hours

rexpectively. Compare their rates of disintegration after 18 hours.