12th physics ppt

2. Topic 15 :
Structure of Atoms
and Nuclei
2

3. 3
15.1 Introduction:
1) Leucippus and Democritus- Every matter
indivisible particles called Atoms.
2)J.Dalton - 1.matter is made of indestructible particles.
2.Atoms of given element are identical. 3.Combination
of atoms form new substance.
3)J.J.Thomson -
4)E.Rutherford-
5)N.Bohr-
is made of

4. 4
15.2 THOMSON’S ATOMIC MODEL :
Glass vacuum tube experiment:
• If voltage is applied across cathode and anode then electrons are emitted
by the cathode.
Plum-pudding model of atom:
• Atom is positively charged sphere in which negatively charged electrons
are embedded.
• In atom, the total positive charge is equal to total negative charge

5. 15.3 GEIGER – MARSDEN EXPERIMENT :
• Diagram:
Observations:
• Most of α particles passes through gold foil without deviation.
• Few α particles are deflected through various angles.
• Very few are reflected back from gold foil.
5

6. 6
15.4 RUTHERFORD ATOMIC MODEL :
• Every atom consist of a positively charged core called nucleus.
• Total mass and positive charge of atom is confined in the nucleus.
• The negatively charged electrons are revolving around the nucleus in circular orbits.
• The total positive charge on nucleus is equal to the total negative charge on revolving electrons.
• The size of nucleus is very small as compared to size of atom.
LIMITATIONS:
• It could not explain stability of atom.
• It could not explain origin of atomic spectra(line spectra).

7. 15.6 N.BOHR’S ATOMIC MODEL :
• The electrons revolves around the nucleus in circular orbits.
• The radius of orbit of an electrons can only take certain fixed values such that the angular momentum of
electron in these orbit is an integral multiple of h/2π.(h=planks constant)
• Electron can make transition from one its orbit to another orbit having lower energy. here it emits a photon
of energy equal to difference between energies of two orbits.
7

8. 15.6.1 Radii of the orbits :
By using Bohr’s theory
from above equations, we get
here radius of Bohr’s orbit is directly proportional to square of principle quantum number.
8

9. 15.6.2 ENERGY OF THE ELECTRONS :
• The total energy of an orbiting electron is the sum of its kinetic enrgy and its
electrostatic potential energy. Thus ,
En = K.E. + P.E. , En being the total energy of electron in nth orbit
𝐸𝑛 = 𝑒 𝑛
1 𝑍𝑒2
2 4𝜋𝜀0𝑟𝑏
9
𝑚 𝑣2 + (− )
• The ionization energy of an atom is the minimum amount of energy required
to be given to an electron in ground state of that atom to set the electron free.
It is the binding energy of the hydrogen atom

10.  ENERGY LEVEL DIAGRAM
10

11. 11
15.6.3 LIMITATIONS OF BOHR’S MODEL :
• It could not explain the line spectra of the atoms other than hydrogen. Even for
hydrogen , more accurate study of observed spectra showed multiple components
in some lines which could not be explained on the basis of this model.
• The intensities of the emission lines seemed to differ from liner to line ang Bohr’s
model had no explanation for that.
• On theoretical side also the model was not entirely satisfactory as it arbitrarily
assumed orbits following a particular condition to be stable. There was no
theoretical basis for that assumption.

12. 15.6.4 De Broglie’s Explanation :
• De Broglie suggested that instead of considering the orbiting electron inside atom as
particle, we should view them as standing waves.
• As light has dual nature material particles also have dual nature i.e. wave and particle
• Wavelength of De Broglie wave is given by formula,
…….(1)
• The relation between De Broglie wavelength and linear momentum is given by ,
• From equation (1) ,
12

13. • Angular momentum of electron in nth orbit is given by ,
Which is nothing but second postulate of Bohr’s atomic model.
Figure : Standing electron wave for
the 4th orbit of an electron in an
atom
13

14. 15.7 Atomic Nucleus :
15.7.1 Constituent of the Nucleus :
• Atomic nucleus is made up of subatomic particles called proton and neutrons , together
they are called nucleons.
• Mass of proton is about 1836 times that of the electron. mass of neutron is nearly same as
mass of proton but slightly greater than mass of proton.
• Proton is positively charged with magnitude of charge is same as the magnitude of charge
of electron.
• Neutron is electrically neutral.
• The number of protons(/electron in neutral atom) in an atom is called its atomic number
and designated as Z. number of neutron is denoted by N.
• The total number of nucleons in a nucleus is called the mass number of atom and denoted
by
𝑍
A= Z+N, therefore atom of an element is denoted as 𝐴𝑋 symbols for hydrogen, carbon and
oxygen can be written as
1𝐻, 12𝐶, 16𝑂.
1 6 8
• The chemical properties of an atom is decided by the number of electron present in it, i.e.
Z. 14

15. 15
• Isotopes :
Atoms having same number of protons but different number of neutrons are called as
isotopes.
Example :
1] deuterium (1𝐻) and tritium (1𝐻) are isotopes of each hydrogen.
2 3
2] 3𝐻𝑒 and 4𝐻𝑒
2 2
• Isobars:
The atom having same mass number A, are called isobars.
Example :
3𝐻𝑒 and 3𝐻𝑒 are isobars .
1 2
• Isotones :
Atoms having the same number of neutrons but different value of atomic number Z,
are called isotones
Example:
3𝐻 and 4𝐻𝑒 are isotones .
1 2

16. Units for measuring masses of atoms and
subatomic particles :
• There three different units of measurement of masses:
• First unit is usual kg , in this system masses of electron, proton and neutrons, me, mp and mn
respectively are .
• Kg is not Convenient method for measurement of masses of subatomic particles .therefor, another
unit called the unified atomic mass unit(u) is used.
“ 1 u is equal to the 1/12th of mass of neutral carbon atom having atomic number
12, in its lowest electronic state. ( 1 u =1.6605402 x 10-27 kg)
In this unit the masses of above three particles are
16

17. • The third unit is in terms of amount of energy that their masses are equivalent to.
Unit used for measurement of masses is eV/c2
one atomic mass unit is equal to 931.5 MeV/c2
The masses of three particles in this unit are
17

18. 15.7.2 Sizes of Nuclei :
•The size of nucleus depends on the number of nucleons present in it i.e. on its atomic number A.
From experimental observations it is found that the radius Rx of a nucleus X is related to the A as
Rx = R0 A1/3 ,
The density ρ inside a nucleus is given by
Where R0 = 1.2 x 10-15 m
Where m = average mass of nucleons. Density is then given as
Putting the value of Rx ,we get
• Thus the density of a nucleus does not depend on the atomic number of the nucleus and is the same for all
nuclei.
the value of nuclear density is ρ = 2.3 x 10 17 kgm-3
18

19. 19
15.7.3 Nuclear Forces :
• Out of these four , the force that determines the structure of the nucleus is the strong force ,
also called the nuclear force.
• This act between proton and neutrons and mostly attractive.
PROPERTIES :
1. It is the strongest force among subatomic particles. Its strength is 50-60 times larger than
that of the electrostatic force of attraction.
2. The nuclear force has a range of about a few fm and the force is negligible when two
nucleons are separated by larger distance.
3. Nuclear force is independent of the charge of the nucleons

20. 15.8 Nuclear Binding Energy :-
• Amount of energy required to separate the nucleons from each other and take them to a large
distance is called the binding energy.
Binding energy is given by,
Where is called mass defect and given by formula,
Here , Z = atomic number
N = neutron number
M = mass of proton
mp = mass of proton
mn = mass of neutron
20

21. • Binding energy per nucleon as a function of mass number :
• EB/A can be used to compare the stabilities of
nuclei. Higher the EB/A value higher the
stability.
• Binding energy per nucleon for different values
of A are plotted in figure shown.
• Deuterium nucleus has the minimum value of
EB/A and is therefore, the least stable nuclei.
• The value of EB/A increases with increase
atomic number and reaches plateau for A
between 50 to 80 . Thus nuclei of these
elements are the most stable among all the
species.
• The peak occurs around A = 56 corresponds to
the iron , which is thus most stable nuclei.
• The value of EB/A decreases gradually for values
of A greater than 80. making the nuclei of those
elements slightly less stable.
• binding energy of hydrogen nucleus having a
single proton is zero. 21

22. 22
15.9 Radioactive Decays:-
• Many of the nuclei are stable i.e. they can remain unchanged for a very long time. Other nuclei
occurring in nature , are not stable and undergoes changes in their structure by emission of
some particle. They change or decay to other nuclei in the process. The decaying nucleus is
called the parent nucleus while the nucleus produced after the decay is called the daughter
nucleus. The process is called radioactive decay or radioactivity.
Alpha Decay :
• In this type of decay, the parent nucleus emits an alpha particle which is the nucleus of
helium atom. The parent nucleus thus loses two proton and two neutrons. The decay
can be expressed as
𝑧 𝑍−2
𝐴𝑋 → 𝐴−4𝑌 + α
Example :
83 81
212𝐵𝑖 → 208𝑇𝑙 + α

23. • the total mass of the product of an alpha decay is always less than the mass of the parent atom. The
excess mass appears as the kinetic energy of the product.
• The difference in the energy equivalent of the mass of the parent atom and that of the sum of masses of
the products is called the Q-value.
• Q value of the decay is equal to the kinetic energy of the products and can be written as
mX, mY and mHe are the masses of the parent atom, the daughter atom and the helium atom.
Beta Decay :
• In this type of decay the nucleus emits an electron produced by converting a neutron in the nucleus
into a proton. The basic process which takes place inside the parent nucleus is
n p + e- + antineutrino
Neutrino and antineutrino are the particles which have very little mass and no change.
• In beta decay there is no change in mass number but atomic number is increased by one.
23

24. • There is another type of beta decay called the beta plus decay in which a proton gets converted to a
neutron by emitting a positron and a neutrino.
• Positron is a particle with the same properties as an electron except that its charge is positive. It is
known as the antiparticle of electron. This decay can be written as,
p n + e+ +neutrino
In this process mass number remains unchanged during the decay but atomic number(Z)
decreases by one. Neutron number(N) increases by one.
The decay can be written as
This decay cannot takes place for a free electron. It can takes place for a proton is inside the nucleus
as the extra energy needed to produce a neutron can be obtained from the rest of the nucleus.
The Q value for the decay can be written as ,
24

25. 25
Gamma Decay :
• In this type of decay, gamma rays are emitted by the parent nucleus. Gamma ray are high energy
photons.
• The daughter nucleus is same as the parent nucleus as no other particle is emitted, but it has less energy
as some energy goes out in the form of the emitted gamma ray.
• Similar to the electrons , the nucleons occupy energy levels with different energies in nucleus. A
Nucleon can make a transition from a higher energy level to a lower energy level, emitting a photon in
the process.
• This energy difference in atom is of few eV’s but for nucleus this difference is of few KeV’s MeV’s .
Therefore radiations emitted by the atom are in the ultraviolet to radio region, the radiations emitted by
nuclei are in the range of gamma rays.
• Usually gamma decay occur after alpha or beta decay , because gamma decay requires large amount of
energy for excitation of nucleus . A nucleon end up in an excited state as a result of the parent nucleus
undergoing alpha or beta decay.
Example : 57Co undergoes beta plus decay to form the daughter nucleus 57Fe which is in excited state
having energy of 136 KeV. This excited nucleus make transition to the ground state by emitting gamma
rays .

26. 15.10 Law of Radioactive decay :
Law of Radioactive decay : At any instant, the rate of radioactive disintegration is directly
proportional to the number of nuclei of the radioactive element present at that instant.
Derivation :Let N0 be the number of nuclei present at time t=0 and N the number of nuclei present
at time t.
𝑑
𝑡
From the law of radioactive decay, 𝑑𝑁
α N
𝑑
𝑡
⸫ 𝑑𝑁
= -λN
𝑁
⸫ 𝑑𝑁
= -λ dt …. (i)
Where, λ is a constant of proportionality called the radioactive decay constant or the disintegration
constant.it is a constant for a particular radioactive element. The minus sign indicates that N
decreases as t increases.
Integrating equation (i)
0 0 0
𝑁ο 𝑡 𝑡
‫׬‬ 𝑑𝑁/𝑁= -‫׬‬ λdt = -λ‫׬‬ 𝑑t
⸫ loge N – loge N0 = -λt
⸫ loge{ 𝑁
} = - λt …..(ii)
⸫
𝑁
𝑁0
𝑁0
= e-λt
⸫ N = N0 e –λt
This is the exponential form of the law of radioactive decay, it shows that the number of nuclei
present decreases exponentially with time.
26

27. The activity of a radioactive element is equal to its rate of designation. In other word we can
say that, number of decays per unit time is called as activity A(t) and is given by
Activity (A) = (-dN/dt)
Activity of the sample after time t,
A= A0 e –λt
Its SI unit is Becquerel (Bq)
Its other units are Curie and Rutherford.
1 Curie = 3.7 X 1010 decay/s
1 Rutherford = 106 decay/s
27
 Activity of a Radioactive Element :

28. 28
15.10.1 Half-life of Radioactive Material :
• The time taken for the number of parent radioactive nuclei of a particular spices to reduce to half
its value is called the half-life T1/2 of the species.
This can be obtained from equation
N (t) = N0e-λt
eλT1/2 = 2
or T1/2 = log 2
= 0.693
λ λ
• In the half-life is that even though the number goes down from N0 to N0 /2 in time T1/2, after
another time interval T1/2 the number of parent nuclei will not go to zero.
• It will go to half of the value at t = T1/2 i.e. to N0 /4.Thus,in a time interval equal to half-life, the
number of parent nuclei reduces by a factor of ½.

29. Average life or mean life (τ) of a radioactive element is the ratio of total life time of all the atoms
and total number of atoms present initially in the sample.
The number of nuclei decaying between time t and t+dt is given by λN0e-λt dt The life time of
these nuclei is t. thus the average lifetime of a nucleus is
τ =
𝑁 0
0 0
1 ∞ ∞
‫׬‬ 𝑡λN e-λt dt = λ
‫׬‬ 𝑡e−λt 𝑑𝑡
Int0
egrating the above we get
τ = 1
λ
The relation between the average life and half life can be obtained as
T1/2 = τlog2 =0.693τ
15.11 Nuclear Energy :
15.10.2 Average Life of Radioactive Species :
• Nuclear energy is the energy released when nuclei undergo a nuclear reaction i.e.
when one nucleus or a pair of nuclei, due to their interaction, undergo a change in
their structure resulting in new nuclei and generating energy in the process.
We can obtain nuclear energy by two other processes
i) nuclear fission in which a heavy nucleus is broken into two nuclei of smaller masses
and
ii) nuclear fusion in which two light nuclei undergo nuclear reaction and fuse together
to form a heavier nucleus. 29

30. • The process of the splitting of a heavy nucleus into two or more lighter nuclei is called nuclear
fission.
When a slow moving neutron strikes with a uranium nucleus a (92U235) it splits into (56Ba141)and
(36Kr92)along with three neutrons and a lot of energy.
15.11.2 Nuclear Fusion :
The process of combining of two lighter nuclei to form one heavy nucleus is called nuclear fusion.
In this process a large amount of energy is released.
Nuclear fusion takes place at very high temperature approximately about 107 K and at very high pressure
106 atmosphere.
Hydrogen bomb is based on nuclear fusion.
30
15.11.1 Nuclear Fission :

31. • A nuclear reactor is an apparatus or a device in which nuclear fission is carried out in a controlled
manner to produce energy in the form of heat which is then converted to electricity.
• In uranium reactor, 92U235 is used as the fuel. It is bombarded by slow neutrons to produce 92U236
which undergoes fission.
Nuclear Chain Reaction :
If the particle starting the nuclear fission reaction is produced as a product and further take
part in the nuclear fission reaction, then a chain of fission reaction started, which is called
nuclear chain reaction.
Nuclear chain reaction are of two types
i) controlled chain reaction
ii) uncontrolled chain reaction.
31
Uranium Nuclear Reactor :

32. Question Bank
Multiple choice questions ( one mark questions)
1) Rate of disintegration of radioactive nucleus is affected by……..
a) temperature
c) external electric or magnetic field
2) In a radioactive decay………
a) only charged material particles are emitted
c) charged material particles as well as energy is emitted
3) Half life of an element depends upon…….
b) pressure
d) none of the above
b) only energy is emitted
d) nothing is emitted
a) original amount
c) temperature
b)external pressure
d)none of the above
4)A radioactive substance has half-life of 4 days. Time required for 31/32 of the original amount to
disintegrate
is……
a) 4 days b)16 days c)20 days d)24 days
5) A radioactive element decays to 1/8th of its initial amount in 75 days. The half life of the element is………
a) 37.5 days b)6.5 days c) 25 days d) 12.5 days
Answer keys:- 1) d 2) c 3) d 4) c 5) c
32

33. 33
Q. Define the following terms.
(1 mark)
1. Ionization energy
2. Isotopes
3. Isobars
4. Isotone
5. Mass defect
6. Binding energy of nucleus
7. Radioactive decay
8. Q- value
9. Radioactivity
10. decay constant
11. Half life period

34. 34
Two Marks Questions :-
1. State postulates of Bohr’s atomic model.
2. State difficulties faced by Rutherford atomic model.
3. Derive the formula for half life period.
4. State and explain nuclear fission.
5. State and explain nuclear fusion.
6. Prove that nuclear density is same for all nuclei.
7. Define binding energy of nucleon and write its expression.

35. 35
Three Marks Question :-
1. Derive the expression for energy of electron in atom.
2. State limitations of Bohr’s atomic theory.
3. State the law of radioactive decay. Derive the formula.
4.Define decay constant and show that it is reciprocal of time duration (t) in which the
substance decays to 37% of its original quantity.
5. Define binding energy of nucleon. State its significance.
6. State types of radioactivity. OR what are alpha, beta and gamma decay.
7. Draw a binding energy curve to show the variation of binding energy per nucleon with
mass number. What are the conclusions can be drawn from B.E curve?

36. Numerical:-
1.
36
2.
• HINT:
Given: mAm = 244.06428 u ; AAm = 244 ,
N(P) = 95 , N(n) = 244 -95 =149
To find : Binding energy per nucleon(EB/A)
Formula : EB = [∆M]c2
• HINT:
Use : Q = [∆M]c2 in each case.
i. Q = [Mra-Mpb-MC]c2
ii. Q = [MU-MBa-MKr-2 x mn]c2
C B e+
iii. Q = [M -M -M ]c2
2.

37. 3.
4.
• HINT: Aavg mass of Mg = 24.312 u:
Formula;
Avg mass og Mg =m(24
12𝑀𝑔) x 78.99
+ m(25
100 12𝑀𝑔) x 𝑥
100
+
12
m(26𝑀𝑔) x 21.01−𝑥
100
Isotope Mass(u) Abundance(%)
24𝑀𝑔
12 23.98504 78.99
25𝑀𝑔
12 24.98548 x
26𝑀𝑔
12 25.98259 (21.01 – x)
• 𝐻𝐼𝑁𝑇: 𝐸𝐵 = ∆𝑀 𝐶2 , ∆𝑀 = 𝑍𝑀𝑃 + 𝑁𝑚𝑛 − 𝑀
= 2𝑚𝑃 + 2𝑚𝑛 − 𝑚𝛼
5.
• HINT: To find, Energy released in
the nuclear reaction. (Q value)
𝑄 = 𝑚𝑝𝑎𝑟𝑒𝑛𝑡 − 𝑚𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑐2
= [𝑚𝐿𝑖 + 𝑚𝑃 − 2𝑚𝛼]𝑐2
37

38. 38
6. Activity of a radioactive element is reduced by 0.75 of its initial value in 2.5 years. Find decay
constant.
ANS: 0.5546year-1
Hint –N=N0e-λt,
7. The decay constant of radioactive substance is 4.33 x 10-4
per year. Calculate its half life.
ANS: 1600 years
Hint T=0.693/λ ,

39. 9. Sample of carbon obtained from any living organism has a decay rate of 15.3 decays per gram per
minute.
A sample of carbon obtained from very old charcoal shows a disintegration rate of 12.3
disintegrations per gram
per minute. Determine the age of the old sample given the decay constant of carbon to be 3.839 x
10 -12 per second .
ANS: 1803 years
𝑑
𝑡
0
HINT: 𝐴 𝑡 = − 𝑑𝑁
= λ𝑁 𝑡 = λ𝑁 𝑒−λ𝑡, 𝐴0 = λ𝑁0𝑒−𝜆 0
39
= λ𝑁0
88
8. The half life of Ra is ‫׬‬
226
1620 𝑦 .Find its decay constant in SI unit.
(Hint T=0.693/λ )
ANS: 1.356 X 10-11 s-1

40. 40
10. Complete the following equations describing nuclear decay
88
a. 226𝑅𝑎 → 𝛼 + … … …
8
b. 19𝑂 → 𝑒− + … … …
90
c. 228𝑇ℎ → 𝛼 + … … …
d. 12𝑁 → 12𝐶 + … … …
7 6
Solution:
a. 226𝑅𝑎 → 𝛼 + 𝟐𝟐𝟔𝑹𝒏
88 𝟖𝟔
b. 19𝑂 → 𝑒− + 𝟏𝟗𝑭
8 𝟗
c. 228𝑇ℎ → 𝛼 + 𝟐𝟐𝟔𝑹𝒂
90 𝟖𝟖
d. 12𝑁 → 12𝐶 + 𝒆+
7 6

41. 11. Disintegration rate of a sample is 1010 per hour at 20 hrs from the start. It reduces to 6.3
x 109 per hours after 30 hours . Calculate its half-life and the initial number of radioactive
atoms in the sample.
ANS: 15 hrs , 5.45 x 1011
𝑑
𝑡
0
HINT: : 𝐴 𝑡 = − 𝑑𝑁
= λ𝑁 𝑡 = λ𝑁 𝑒−λ𝑡, 𝐴0 = λ𝑁0𝑒−𝜆 0 = λ𝑁0
15
2
12. A source contains two species of phosphorous nuclei, 32𝑃 (𝑇1 = 14.3 𝑑𝑎𝑦𝑠) and
15
2
32𝑃 (𝑇1 = 14.3 𝑑𝑎𝑦𝑠) .
15
At time t = 0, 90% of the decays are from 32𝑃. How much time has to elapsed for only 15% of the
15
decays to be from 32𝑃 ?
ANS: 186.6 d
HINT: find λ1 𝑎𝑛𝑑 λ2 by using formula λ =
0.693
𝑇
𝑑
𝑡
0
41
: 𝐴 𝑡 = − 𝑑𝑁
= λ𝑁 𝑡 = λ𝑁 𝑒−λ𝑡,

42. Portion deleted due to Covid-19 for the year 2020-2021
42
Sr.no Page Number . Article
01 324 15.3 Geiger Marsden
experiment
02 330-332 15.7 Atomic nucleus
03 332-333 15.8 Nuclear binding energy
04 333-336 15.9 Radioactive decay
05 338-341 15.11 Nuclear energy

43. 43
Topic: Structure of Atom and Nuclei
PPT Presentation By-
- Mr. Mote D.P.
New Model Junior
college , Kolhapur.
- Mr. Halli S.A.
New Model Junior
college , Kolhapur.
- Mr. KirdatN.S.
Shri. Venna Vidyamandirand
JuniorCollege, Medha, Satara

44. 44