Download Radioactivity

By C K Cheung
Radioactivity
Radioactivity is the spontaneous disintegration (= decay) of the nucleus of an atom, from
which may be emitted some or all of the followings:
1/  -particle
2/  -particle
3/  rays
This spontaneous process is not affected by:
a/ chemical combination (e.g. ________________)
b/
physical environment (e.g. _____________________)
Experiment
1000 identical cubes with
one marked surface
Marked face uppermost
 ‘decayed’ and will be
taken away.
away
Repeat the experiment until only a few cubes have not ‘decayed’
number of
undecayed
cubes
number of throw
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By C K Cheung
Law of Radioactive Decay
The rate of disintegration of a given nuclide at any time is directly proportional to the
number of nuclei, N, of the nuclide present at that time.
dN decayed
dt
No. of radioactive
nuclei = No
Hence,
dN
N
dt

dN
 (cons tan t )( dt )
N

dN
 ( )dt
N
If
at t = 0, N = No
1/
2/
dN = change in number of undecayed nuclei
 called decay constant > 0
at t = t, N = N
N


N0
 ln(

t
dN
   dt
N
0
N
)=-t
N0
N = N0 e t
number of undecayed nuclei
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By C K Cheung
N
~e
 t
t
0
Note:
 dN
 dN
 N  probability for a nucleus to decay per unit time is constant
1/  =
Ndt
dt
..\powerpoint\meaning of decay constant.ppt
1st
2nd
2/
 dN
 N  Activity (A)
dt
A = A 0 e t
e.g.
A radioactive sample has T = 5600 yrs. Find the time taken for
1
of
16
the sample to decay.
521 yrs.
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By C K Cheung
Half-life ( T )
Time required for half of the sample to decay.
λt
∵ N = N0 e N
 e  t
∴
N0

1
 e2
λT
 -  T = lne(
1
)
2
  T = lne( 2 )
∴ λ =
ln( 2)
T
Background Radiation.
A /counts s-1
A0
AT
Ab
T
time
AT =
A0  Ab
 Ab
2
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By C K Cheung
Properties of 3 radiations

Property
Nature
Mass (atomic mass
unit /amu)
Effect on
photographic plate
number of ion-pairs
per mm in air
(ionization power)
Absorption
(stopped by up to)
(penetration power)


Helium nuclei
electrons
EM radiation with
very short wavelength
4u
u
1840
0
Yes
Yes
Yes
~104
~102
~1
~cm air
~10 – 2 mm Al
~mm Al foil
~ sheet of paper or
skin
~ cm Pb
Speed (ms – 1)
~107
~107 - 108
Effect of B & E
Bent slightly
Bent strongly
No effect
Disperse considerably
(varies)
3x108
Some uses of radioactive isotopes:
1/ Cobalt – 60 emits  - rays which are used for treating cancer, and for
sterilization
2/ As tracer elements: a radioisotope will experience the same chemical
treatment as its non-active isotope, but its activity enables it to be
detected even in minute quantities.
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By C K Cheung
3/ To measure the thickness of a material:
I = I0e - kx
Incident intensity = I0
X
4/ Dating methods
atmosphere
radioactive
14
7N
 01n146C * 11H
N: atmospheric nitrogen
n : ejected from nuclei in atmosphere by cosmic ray
C: radioactive with T1/2 = 5700 yrs.
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By C K Cheung
14 *
6C
 O2  C *O2
C*O2 taken by plants & trees for manufacturer of
carbohydrates in photosynthesis.
The normal activity of living plants ~ 15.3 counts per
minute per gram of carbon. But when the organism dies  no
intake of C*, but decay process goes on with T1/2 ~ 5700
years.
By measuring the activity of some furniture from an ancient village  age of the
furniture can be estimated within the range of 1000 to 5000 years.
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By C K Cheung
Nuclear Fission
When a heavy nuclide is split into 2 large fragments, the process is called fission.
Usually, a fission process requires a neutron ( uncharged ) to initiate it.
Note:
we don’t interest in which the atomic nucleus changes only slightly after
disintegration because the mass defect is small.
But, if the nucleus split into 2 large nuclei, the mass decrease is appreciable.
Consider:
236
( U 92
)
…
235
U 92
+ n 10
236
1
1/ U 92
Xe 140
+ Sr 94
54
38 + 2 n 0 + 200MeV
236
1
2/ U 92
Ba 144
+ Kr 90
56
36 + 2 n 0 + energy
a variety of further decay
a variety of further decay
Called fission neutron
Chain reaction
n
U235
n
U235
n
U235
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By C K Cheung
Fission Reactor
Inside reactor, about 1 fission neutron ( out of
produce 1 another new fission.
2 ) from each fission process can
n
U235
n
n
U235
U235
U235
>
99 % U 238
Natural Uranium
< 1%
U 235
U-238:

Only fission with very fast neutrons

Capture medium-speed neutrons without fissioning. ( undergo -decay )
U-235:

Fissions with slow neutrons.
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By C K Cheung
Nuclear Fusion
Two light nuclei combine together to yield a heavier nucleus, with
release of energy
e.g.
Synthesis of He 42 from 4 H 11 :
H 11 + H 11
H 12 + e  + 0.4 Mev
H 11 + H 12
He 32 + 5.5 Mev
He 32 +He 32
He 42 + 2 H 11 + 12.9 Mev
 chain reaction
Conditions for fusion process:
1/ high density ( to increase the collision chances )
2/ high temperature ~ 108 – 109 K (  the initial light nuclei have enough
K.E. to overcome their mutual repulsion and come close enough to
react).
Note:
How to keep the hot reacting plasma from touching the vessel holding it , still
an unsolved problem.
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By C K Cheung
Mass & Energy
Def.:
1 atomic mass unit ( amu ) = (
 1 amu = (
1
) of the mass of a C12 atom.
12
1
12
1
x
)(
) = 1.66 x 10 – 27 kg
12
1000 6.02 x10 23
 E = mc2
 1 amu = (1.66 x 10 – 27 kg )(3x108 )2 = 1.494 x 10 – 10 J
Also, 1 eV = 1.6 x 10 –19 J
 1 amu = 931.478 MeV
Binding Energy
Mass of neutron = mn
Mass of proton = mp
Mass of nucleus = m
It is found that :
mass of nucleus <
sum of mass of individual nucleon
Phenomenon called mass defect
Note:
1/
2/
3/
m  binding energy of nucleus < 0
dU
F= short-range nuclear attractive force.
dr
Ionization energy = - binding energy
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By C K Cheung
Binding Fraction ( B.F. )
B.F. =
B. E .
= binding energy per nucleon
A
B.F. increases  nucleus more stable
B.F./MeV
8.5
fission
fusion
Fe-55
A ( mass number)
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