Notes for Atoms Molecules and Nuclei - Part III

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Atoms, Molecules and Nuclei
Q.63 The de-Broglie wavelength of a particle having a momentum of 2×10-28kg m/s is
(a.63) 3.3×10-5m (b.63) 6.6×10-6m (c.63) 3.3×10-6m (d.63) 1.65×10-6m
Q.64 A proton and an α particle are accelectrated through the same potential difference. The ratio
of the de-Broglie wavelength of the proton to the de-Broglie wavelength of the α particle will
be
(a.64)
(b.64)
(c.64)
(d.64)
Composition And Size Of Nucleus
Nucleus: - positively charged and high density centre.
99.9% mass of the atom.
Protons(+ve) + neutrons(neutral)= nucleons
number of protons = atomic number (Z).
number of protons & neutrons = mass number(A).
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nucleus symbolically expressed as A X
Z
For example, gold: - 197 A u and Uranium: 79
238
92
U.
Radius of nucleus
1
R = R0 A 3 where R0 is linear constant = 1.2 × 10-15 m.
volume of nucleus α A.
Density of nucleus is constant = 2.3 × 1017 1kg/m3,
radius of carbon nuclei is
1
R C = 1 .2 ´ 1 0
- 15
= 2 .7 4 7 3 ´ 1 0
m ´ (1 2 ) 3
- 15
m
Radius of uranium nuclei is
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1
R U = 1 .2 ´ 1 0
- 15 m
= 7 .4 3 6 6 ´ 1 0
´ (238 )3
- 15
m
Isotopes, isotones and isobars
Isotopes: - The nuclei have same number of protons
but different number of neutrons. E.g. deuterium 21 H ,
tritium 31 H are the isotopes of hydrogen. gold has 32
isotopes. Isotopes have identical chemical behavior
and are placed in the same location in the periodic
table.
Isobars: - The nuclei have same mass number (A). For
example, the nuclei 31 H , 3 H e are isobars.
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Isotones:- The nuclei having same number of neutrons
(A – Z) but different atomic numbers Z. For example
198
80
Hg,
179
79
A u , are isotones.
Mass-Energy relation
Einstein proved that mass is a form of energy.
E = m c2
Energy of electron.
Ee = mec2= (9.1 × 10-31) × (3 ×108)2 joule
=
9 .1 ´ 9 ´ 1 0
- 31
1 .6 ´ 1 0
´ 10
- 19
16
eV
= 0.511 × 106 eV = 0.511 MeV
Similarly, the energies of proton and neutron are
Ep = 941.1 MeV and En = 942.2 MeV
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There is one more unit used to express nuclear
masses. It is Unified atomic mass unit. It is (1/12)th
of the mass of neutral carbon atom in its lowest
energy state. Its symbol is ‘u;
1u = 1.66054 × 10-27 = 931 MeV/C2
OR Energy equivalent of mass 1 u is = 931 MeV
Mass Defect
It is observed that the mass of a nucleus is smaller
than the sum of the masses of constituent nucleons in
the Free State. The difference between the actual
mass of the nucleus and the sum of masses of
constituent nucleons is called mass defect.
Let
M –
be the measured mass of nucleus.
A –
be the mass number (mass of
nucleons in free state)
Z
-
atomic number (number of protons)
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Mp -
mass of hydrogen atom (i.e. proton)
Ma -
Mass of free neutron
(A – Z) - number of neutrons.
The mass defect △m = [Zmp = (A – Z)mn] – M
Nuclear Binding Energy
Nucleons (protons and neutrons) are bound together in
a nucleus with very strong attractive force. Energy
must be supplied to the nucleus to separate its
constituent nucleons. It is observed that mass of the
nucleus is always less than the sum of the masses of
its constituent nucleons. The difference in mass is
being used as energy that holds nucleons together.
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The amount of energy required to separate all the
nucleons from the nucleus is called binding energy of
the nucleus.
The B.E. of nucleus is very high. For example, it is 2.22
MeV for deuteron nucleus, whereas B.E. for an atom,
say hydrogen atom in its ground state is 13.6 eV. That
is, B.E. of nucleus is about 10,00,000 times larger than
B.E. of atom.
The B. E. of nucleus can be expressed in terms of
mass defect. B.E. = △m × c2 joule
Where △m is mass defect and c is speed of light.
But △m = [Zmp + (A – Z)mn] – M
∴ B. E. of nucleus = [Zmp + (A – Z)mn – M]c2 joule
The B.E. per nucleon =
B. E. o f n u cle u s
A
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E =
éZ m p + ( A - Z )m n - M ù 2
ê
úc
ê
ú
A
ë
û
This is average energy per nucleon to separate a
nucleon from the nucleus.
B.E. Curve
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The B.E. curve is an indicator of nuclear stability. The
higher the B.E. per nucleon, the greater is the stability
From B.E curve we can infer as follows:
i.
The B.E. per nucleon is practically constant and
is independent of mass number for nuclei,
30 < A < 170.
ii.
It is maximum 8.75 MeV, for A = 56 and is 7.6
MeV, for A = 238.
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iii. It is low for both light nuclei (A < 30) and heavy
nuclei (A > 170). This means that the nucleons of
atoms are loosely bound with nucleus.
iv. When heavy nucleus (A = 240) breaks into lighter
nuclei (A = 120), B.E. increases i.e. nucleons get
more tightly bound.
v. When very light nuclei A < 10, join to form a heavier
nucleus, B.E. increases, i.e. nucleons get more
tightly bound.In both the cases, there is release of
energy because, the new nuclei formed have less
mass and are more stable.
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Radioactivity
Becquerel
Heavy elements like uranium, radium having A > 82
are unstable and emit highly penetrating radiations.
The substances which emit these radiations are known
as radioactive substances.
The
phenomenon
of
spontaneous
emission
of
radiations from radioactive substance is known as
radioactivity.
Radioactivity is property of atom and nuclei, hence is
unaffected
by
chemical
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or
physical
changes.

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Radioactivity is nuclear phenomenon in which an
unstable nucleus undergoes decay. It is called
radioactive decay.
There are three types of decay –
i.
-decay - 4 H e .
2
ii.
-decay - electrons or positrons.
iii.
-decay - high energy photons.
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Properties of –particles
1. +ve. It is helium atom with both electrons removed.
Mass:- 6.64×10-27kg & charge +3.2×10-19 coulomb.
2. It is deflected by electric and magnetic field.
3. The speed of emission of
-particles depend upon
the nature of radioactive element. It varies from
(1/10)th to (1/100)th of the speed of light.
4. Affect photographic plate, produce fluorescence.
5. They ionize gas when passed through gas.
6. Range:- through air:- 2.7cm to 8.62cm for thorium.
7. They are scattered when incident on mica,
aluminium and gold foil.
8. When an
-particle is emitted by an atom, its
atomic number decreases by 2 and mass number
decreases by 4.
e.g.
238
92
U ®
234
90
Th +
4
2
He
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Properties of -particles
1.
-rays are fast moving electrons
2. Their speed ranges from 1% to 99% of the speed of
light.
3. Being charged particles they are deflected by
electric and magnetic field.
4. They can ionize gas but its ionization power is
th
æ 1 ö
÷ of that of
ç
÷
ç
÷
ç1 0 0 ø
è
-particles.
5. They are more penetrating than -particles.
6. Their range in air depends on their speed. A
-
particle of 0.5 MeV has a range of 1 m in air.
7. When
-particle is radiated, the atomic number
increases by 1 and mass number does not change
e.g.
32
15
P ®
32
16
S + 1e
0
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Properties of -rays
1.
-rays
are
not
particles
but
they
are
electromagnetic waves (photons) of very short
wavelength. Photons originating from the nucleus
are called -rays.
2. They are neutral in charge and not affected by
electric and magnetic field.
3. They
affect
photographic
plate
and
produce
fluorescence.
th
æ 1 ö
÷
4. They have very low ionization power about ç
ç
÷
ç1 0 0 0 ÷
è
ø
of that of σ a-particles.
5. They have high penetration power and can pas
through 25cm thick iron plates.
6. They are diffracted by crystals.
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Radioactive Decay law
The spontaneous breaking of nucleus is known as
radioactive disintegration.
They decay law
The number of nuclei undergoing the decay per unit
time is proportional to the number of unchanged nuclei
present at that instant.
Let N be the number of nuclei present at any instant t,
dN be the number of nuclei that disintegrated in short
interval of time dt. Then according to decay law:
-
dN
dt
a
N
i.e.
dN
dt
= - l N
(1 )
Where λ is known as decay constant or disintegration
constant.
From equation (1)
dN
N
= - l dt
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Integrating both sides
ò
dN
N
=
ò-
l dt
loge N = –λt + c
where c is constant of integration whose value
depends on initial conditions.
At t = 0; N = N0 (the number of original nuclei)
∴ loge N0 = 0 + c
Substitution the value in above expression
loge N = – λt + loge N0
= – λt
loge N – loge N0
lo g e
æN ö
ç ÷ = ç ÷
çN ÷
è 0÷
ø
N
N0
Or
= e
l t
-
l t
N = N0 e-λt
...(2)
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This expression shows that number of nuclei of
given radioactive substance decreases exponentially
with time.
Decay constant
From equation (1) we have
dN
l =
-
dt
N
The decay constant is defined as ratio of the
amount of substance disintegrated per unit time to
amount of substance present at that time.
We have N = N0e-
t
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Let us define ‘t’ as t =
1
1
N
N0 e
N = N0e-1
N =
N =
N0
e
N0
2 .7 1 8
N = 0.37 N0
1
The decay constant , which is equal to , can be
t
defined as reciprocal of time duration (t) in which the
substance decays to 37% its original quality.
Half life period (T)
Half life period (T) of radioactive substance is
defined as the time in which the half substance is
disintegrated.
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We have N = N0eat t = T; N =
∴
or
N0
= N0e-
2
1
= e-
2
or e
t
t
N0
2
T
T
=2
T = loge 2 = 0.693
∴ T
=
0 .6 9 3
l
Using this expression, we can determine the half
life of radioactive substance if its decay constant is
known.
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Nuclear fission
Discovered by:- German scientists Otto Hahn and
Strassman(1939)
235
92
U +
1
0
n ®
236
92
144
56
U ®
22
Ba +
89
36
Kr + 3
1
0
n

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Nuclear fusion
When two lighter nuclei are fused to form a heavier
nucleus, the process is called nuclear fusion.
1
1
H +
2
1
H +
1
1
H ®
2
1
H ®
2
1
4
H + e + 0 .4 2 M e V
4
1
He + 24 M eV
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