Isotopes
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Radioactivity
• 1896: discovery of radioactivity
• 1899: activity of a pure radioactive
substance decreases with time according
to an exponential law
• 1901: the decay is a statistical in nature,
that it is impossible to predict when any
given atom will disintegrate
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• Radioactive
R di
ti D
Decay:
– spontaneous adjustment of the nuclei of
unstable atoms to a more stable form
– transition between 2 possible “states” of a
system
• 20 neutrons, 20 protons, 20 electrons: 40Ca (state 1)
• 21 neutrons, 19 protons, 19 electrons: 40K (state 2)
• state 2 -> state 1 (transition probability = λ)
• Radioactive property depends on its nucleus,
not upon its electron structure
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Types of Radioactive Decay
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α decay (α emission)
• Nuclei emits an α particle
– (N->N-2, Z->Z-2, A->A-4)
• Examples
238U -> 248Th + α
147Sm -> 143Nd + α
234U -> 230Th + α
226Ra -> 222Rn + α
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β decay
• Direct
Di t conversions
i
off
– a proton into a neutron
• (β+ decay p -> n + β+)
• (electron capture: p + β- -> n)
– a neutron into a proton
• (β- decay: n -> p + β-)
• A = constant (isobaric decay)
• Examples 18 F →18O + β +
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8
87
37
87
Rb→12
Sr + β −
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11
Na →1224Mg + β −
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γ decay
•
•
•
•
Transition between nuclear states
Identity of nucleus does not change
Recoil energy is small
All the previously stated decays can
produce daughter nucleus of excited
states -> followed by γ decay
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Fission
• Neutron
Neutron-induced
induced fission
• Spontaneous fission
– 238U (t1/2 = 8.19 E+15 yrs)
– 256Fm ((t1/2 = 2.6 hrs))
– 254Cf (t1/2 = 60.5 hrs)
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Branching ratios and
Partial Half-lives
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Equations of radioactive decay
Terms
λ: decay constant [time-1]
λN: activity [disintegration/time]
1 Curie = 1 Ci = 3
3.7
7 x 1010 decays/sec
t1/2 : half-life [time] = (ln2) / λ
τ: lifetime or mean life [time] = 1/λ
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When we consider decays only (no production of
parent atoms in the system),
(dN/dt)
(d
/d ) = -λ N
λ: decay constant
N: radioactive nuclei present at time t
This equation indicates that “the number dN decaying in a
time dt is p
proportional
p
to N”.
By integrating each side of the eqn,
N(t) = Noe-λt
No: original number of nuclei present at t=0
By putting N=No/2 (when the number of parent nuclei
becomes half of the original)
t1/2 = ln2/λ
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for practical applications to geological materials..
P: # parent atoms currently present in mineral
Po: # parentt atoms
t
when
h the
th mineral
i
l fformed
d
D*: # daughter atoms currently present (radiogenic D)
Po = P + D* (=No)
P=(P+D*) e-λt
t=1/λ ln(1+D*/P) … age equation
assumption: no gain or loss of parent and daughter atoms (closed
system behavior)
-> Can we test this assumption?
-> use Isochron (Rb/Sr, Sm/Nd, Lu/Hf, K/Ar, 40Ar/39Ar,), Age
spectra (40Ar/39Ar), Concordia Diagram (U/Pb)
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When we consider both production and decay of
parent atoms in the system,
(dN/dt) = P(t) -λ
λN
P(t): production rate of parent atom
By integrating each side of the eqn,
N (t ) = N 0 e
− λt
+e
− λt
∫
t
0
P(t ' )e λt ' dt '
If the P(t) = P constant,
∫
t
0
P (t ' )e λt ' dt ' =
[
e ]
λ
P
λt ' t
0
=
(
e
λ
P
λt
)
−1
substituting above,
above
N (t ) = N 0 e −λt +
(
1− e )
λ
P
− λt
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U-Th Decay Chain
White Textbook
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(
)→
→
→
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