Radioactive decay, kinetics and equilibrium

1. RASHTRASANT TUKADOJI MAHARAJ NAGPUR UNIVERSITY
DEPARTMENT OF CHEMISTRY
RADIOACTIVE DECAY, KINETICS,
EQUILIBRIUM
PRESENTED BY: BIJI SARO VARGHESE
M.Sc. II Sem III
4/10/2018 1

2. CONTENTS
1.RADIOACTIVE DECAY
2.RADIOACTIVE KINETICS
3.RADIOACTIVE EQUILIBRIUM
2

3. Radioactive Decay
• Radioactive decay is a spontaneous
phenomenon of emission of particles or
electromagnetic radiation from an atomic
nucleus.
• The phenomenon of radioactivity was
discovered by Henri Becquerel in 1896
and the radiations emitted were called as
Becquerel rays or Uranic rays .
• Pierre and Marie Curie introduced the
term Radioactivity for this phenomenon
3

4. Radioactive decay results in the emission of either:
• an alpha particle (α),
• a beta particle (β),
• a gamma ray(γ)
• or fission fragments
4

5. A nucleus undergoing alpha decay emits
an alpha particle [ ]+2 which is helium
nucleus with two protons and two
neutrons.
Atomic and mass no. of the product
nucleus are reduced by 2and 4 units
respectively.
Alpha Decay
5
2He
4

6. Y
A - 4
Z - 2
+ He +Eα
4
2
unstable atom
more stable atom alpha particle
232
U92 90
228
Th +
4
He +Eα2
6
X
A
Z

7. Beta decay
• In beta decay the charge of the resulting
product nucleus differs from the starting
nucleus by one unit and there is no change in
mass number.
• Beta decay comprises of three processes:
i. Negatron decay(β-)
7
132
I53 54
132
Xe + β-+ ν + Eβ

8. 10
172
Lu71 70
172
Yb + ν
8
ii. Positron decay(β+)
22
Na11
22
Ne + β++ ν + Eβ
iii. Electron capture(EC)

9. Gamma deexcitation
• Alpha and beta decay quite often leave the
daughter product nucleus in excited states.
• When an excited state of a nucleus
undergoes deexcitation ,electromagnetic
radiation, known as gamma rays, is
emitted.
9

10. 60
Co*
29 30
60
Ni* + β- + ν
60
Ni*
30 30
60
Ni + γ
10

11. Spontaneous fission
• Spontaneous fission is a decay process
in which a nucleus undergoes division
into two fragments along with emission
of 2-3 neutrons.
• This is prevalent in isotopes of heavy
elements.
11
252
Cf92
F1 + F2 +3.76neutrons

12. RADIOACTIVE KINETICS
The rate of decay of a radioisotope is
proportional to the number of atoms of that
isotope present at that instant.
Radioactive decay follows the first order
kinetics.
-
𝑑𝑁
𝑑𝑡
=λN ………(1)
where, N=no. of atoms at any time t
λ=disintegration constant (time-)
12

13. On integration of eqn.(1)
N=N0 e-λt ……….(2)
Where, N0 =no. of atoms at the initial time
Radioisotopes are estimated by measuring
radioactivity or simply activity (A),i.e. the
product of decay constant (λ) and the no. of
atoms present (N) rather than N alone
A=Nλ ………….(3)
Activity has unit of disintegration per unit time
The units of radioactivity are:
1 Becquerel(Bq)=1dps
1Curie(Ci)=3.7 x 1010 dps
13

14. Combining equation 2 and 3, a relation for
activity as a function of time is obtained.
A=A0 e-λt ………..(4)
14Fig no.1 Decay scheme of 32P on a linear plot

15. Half life
The time required for the decay of half of the
parent atoms to daughter products is defined as
the half-life(t1/2) of the parent nuclide.
Thus , t=t1/2 when N=N0 /2
Substituting in equation 2 and simplifying we
get,
1
2
= 𝑒
−λt
…………….(5)
And t1/2 =
ln 2
λ
=
0.693
λ
……………(6)
15
1/2

16. Half life of the radioisotope is determined from the
activity profile(fig 1).
Taking log of equation no.4
log A=logA0 -λt ………….(7)
A straight line is obtained when logA is plotted as a
function of time on a semi log paper.
Half – life is a unique characteristic of each isotope.
16

17. Fig no.2 Log of activity as a function of time
17

18. Mean life
The life time of radioactive isotope varies from 0
to∞
The average time that an atom of a radioisotope
can survive is called mean life(τ) which is
obtained by dividing sum of the life times of all
the atoms by the initial number of atoms.
The mean life is given by
τ = -
1
N0
𝑡=0
∞
𝑑𝑁 ………….(8)
18

19. =
1
N0
0
∞
𝑡. λ𝑁𝑑𝑡 = 0
∞
𝑡𝑒−λ𝑡
𝑑𝑡 ………..(9)
By partial integration of equation no. 9 we get,
𝜏 =
1
λ
…………..(10)
19

20. Branching decay
The total decay constant (λ) of the nuclide is
given by the sum of the partial decay constants;
λ=λ1+ λ2 + ….
Let the nuclide X decays to two daughter
products Y and Z, having corresponding decay
constants as λ1 and λ2 respectively.
λ1 Y
X
λ2 Z
λ=λ1+ λ2
20

21. Rate of decay of X is
-
𝑑𝑁
𝑑𝑡
= λ1+ λ2 𝑁 = λN ………..(11)
Total half-life of X is related to partial half-lives as
0.693
t1/2
=
0.693
t1/2
+
0.693
t1/2
Thus the total half-life of X is shorter than any of
the individual partial half-lives.
21
X X ZX Y

22. RADIOACTIVE EQUILIBIUM
The condition of constant ratio of parent and
daughter activity is called equilibrium.
Half life of daughter< half life of parent
But, if
Half life of daughter> half life of parent
Then, no equilibrium
22

23. TRANSIENT EQUILIBRIUM
In the cases where decay constants λ1
(parent) and λ2 (daughter) are in the ratio
of 0.1, the equilibrium is called transient
equilibrium.
A typical example is
23
99Mo 99mTc 99Tcβ- IT
6.01 h65.94 h

24. Fig no.3 Activity profile in a transient equilibrium case
Curve a: total activity of the
parent and daughter
Curve b: represents the decay
of pure parent
Curve c: represents growth of
daughter product
Curve d: extrapolation of c,
represents activity of
daughter
Curve e: (curve c - curve d)
represents the decay of pure
daughter fraction
24

25. SECULAR EQUILIBRIUM
If the half life of the parent isotope is much longer than
the half life of the daughter isotope(λ2>>λ1), then the
equilibrium is called secular equilibrium. In this
condition, the total activity of the parent and daughter
reaches the maximum and does not decrease
appreciably for several half-lives of the daughter
product.
Decay of 144Ce is an example of secular equilibrium.
25
β-
17.28 min
β-
284.893 d
144Ce 144Pr 144Nd

26. Fig no.4 Activity profile in a secular equilibrium case
Curve a: total activity of the
parent and daughter
Curve b: represents activity
due to parent which is equal
to daughter activity
Curve c: represents growth of
daughter activity in pure
fraction
Curve d: represents decay of
the daughter product
26

27. NO EQUILIBRIUM
If the decay constant of parent is larger than that of the
daughter i.e. λ1 > λ2 ,then the parent decays faster than the
growth of the daughter product. This does not satisfy the
equilibrium condition of constant activity ratio at any
point of time after preparing the pure parent sample and
therefore represents a no equilibrium case.
For example, 138Xe is short lived compared to its daughter
product 138Cs.
27
β-
14.08 min 33.41 min
β-
138Xe 138Cs 138Ba

28. Fig no.5 Activity profile in a no equilibrium case
Curve a: total activity of the
parent and daughter
Curve b: represents the decay
of pure parent
Curve c: represents growth of
daughter product
Curve d: extrapolation of c,
represents decay of pure
daughter
28

29. 29
1. D.D.Sood, A.V.R.Reddy and
N.Ramamoorthy, Fundamentals of
radiochemistry, IANCAS publication,
2007
2. H.J.Arnikar, Essentials of nuclear
chemistry, New age international
publishers,2014,Fifth edition

30. 30