Download Nuclear Chemistry

Chapter 19
Nuclear Chemistry
Hill, Petrucci, McCreary & Perry 4th Ed.
Radioactivity
Spontaneous Nuclear Decay
Alpha - α
Beta - β
Gamma - γ
4
2+
He
2
0
-1e
0γ
0
A Helium Cation ejected from .
the nucleus at high energy.
An electron ejected from
the nucleus at high energy. .
High Energy electromagnetic .
radiation.
Radioactivity
Other Types of Nuclear Decay
Positron emission:
Beta(+) - β+
0
+1e
An anti-electron ejected from .
the nucleus at high energy.
Beta(+) - β+
1
p
1
1n
0
+
0
+1e
Beta decay - β
1n
0
1
p
1
+
0
-1 e
Electron Capture - ec - A nucleus captures an
electron from outside.
1
p
1
+
0
-1e
1n
0
.
Nuclear Symbols
Isotope Number
~ At. mass
#n + #p =
235
92 U
Atomic Number
= #p
= nuclear charge
Elementary Particles:
1n
0
;
0γ
0
;
0
-1β
Atomic Symbol
4
2+
He
2
0
or -1e
;
;
1
1H
or 1p
1
0
or 0e
β
+1
+1
Balancing Nuclear Equations
Alpha decay:
Beta(+) decay:
226
88
Ra
95
43
+
Tc
Beta(-) decay:
14
6C
Electron Capture
40
19 K
4
2+
He
2
0
+1 e
+
+
+
0
-1 e
0
-1 e
Can you balance these? The subscript numbers and the
superscript numbers must be algebraically equal on each side of
the arrow.
Transmutation of Elements
Nuclear Bombardment: .
14
N
7
9
4Be
14
7N
+
1H
1
4
2+
He
2
+
1n
0
1n
0
+
1H
1
+
4
2+
He
2
+
+
Supply the missing nuclides!
Neutrons are better particles to bombard the nucleus! Why?
Nuclear Reactions
Determine the missing Nuclide!
Nuclear Fission:
1n
0
235
92U
+
+
94
Kr
36
+ 3 10n
Nuclear Fusion:
2
H
1
+
3
H
1
+
Tritium "T"
Deuterium "D"
1n
0
Nuclear Stability
From the number of Stable Isotopes found in nature:
Proton Numbers that are:
Even
Even
Odd
Neutron Numbers that are:
Even
Odd
Even Odd
Number of Isotopes:
157
52
50
Odd
5
Certain Even Numbers impart Special Stability: "Magic Numbers"
Proton Numbers that have values of:
2, 8, 20, 28, 50, 82 [126]
Neutron Numbers that have values of: 2, 8, 20, 28, 50, 82, 126
4
2He
16
8O
40
Ca
20
208
82 Pb
Observations on Stability and Composition
•Light nuclei up to calcium-40 have a n/p ratio
near 1. Ca-40 n/p = 1,“double magic”
•Heavier nuclei have correspondingly greater
n/p ratios, Bi-209 heaviest stable nuclide has n/p
= 126/83 = 1.52
•Heaviest nuclides decay by alpha decay, lose 4
mass units, slightly increases n/p.
•Neutron rich nuclides, beta decay, n to p.
•Proton rich nuclides, β+ or ec, p to n.
Observations on Stability & Composition
Binding Energy = ∆mc2
•The “most stable” nuclides have mass
numbers between 55 & 60 = Fe through Ni
•Light nuclei have the least binding energy
per nucleon. Magic number effect strong.
•Heaviest nuclei are less stable than mid
range mass nuclei, per nucleon.
Suggest reasons for energetic fusion and fission.
Source of Nuclear Energy: E = ∆mc2
Matter is Converted into Energy
E = ∆mc2
Joule = kg.m2/s2
One must use the "Exact Mass"
of nucleons to calculate ∆m.
∆m =
Σim(products)
c = 3.00 x 10 8 m/s
-
Σjm(reactants)
Where i & j are coefficients in the balanced nuclear equation
and m is the "exact mass" of each nuclide in the equation.
Notice the similarity to the Hess' Law equation for ∆H and ∆G.
If ∆m is negative the reaction is exothermic !
Calculation of Nuclear Binding Energy
Mass Defect = The mass loss on forming the
Nuclide from Neutrons and Protons
From:
∆m = Σim(products) - Σjm(reactants)
This is actually mass loss in formation of a nuclide.
Mass
Defect
=
Exact Mass
of Nuclide
-
Σim(neutrons)
+
Σjm(protons)
Number of neutrons
Number of protons, the "Atomic Number"
To compare nuclide stability with another nuclide you need to divide
each nuclide mass defect by the number of protons + neutrons.
This gives the mass loss per nucleon. Each neutron and each proton
is a constituent nucleon of a nuclide.
Energetics of Nuclear Reactions
See Section 19.7 p 812:
E = mc2
1 u = 1.6606 x 10-27 kg
A mass defect of 1 u (atomic mass unit)
corresponds to 1.4924 x 10-10 Joule.
1 u => E = 931.5 MeV
1 MeV = 1.6022 x 10-13 Joule
Binding Energy is defined as the energy to
decompose a nuclide to neutrons and protons,
its usually expressed in MeV.
Calculating Binding Energy
Calculate the mass defect and binding energy of
3
2 He
Mass
Defect
= 3.01493 u
=
Exact Mass
of Nuclide
mp = 1.00728 u
mn = 1.00867 u
-
Σim(neutrons)
3
2 He
+
Σjm(protons)
Activity & Rates of Decay
Rate of radioactive decay:
A "first order" rate process
A = λN
rate = k[A]1
number of atoms
activity, disentegrations/second
decay constant
A Unit of activity, the Curie, C
1 Ci
i
3.7 x 1010 dis/s
One Curie is the decay rate of 1 gram of Radium-226.
Radionuclides are sold by activity:
mCi and µCi
Half-Life and the Activity
Half-Life = Time required for half the atoms to decay:
0.693
t1 =
2
λ
To calculate the activity and the decay constant:
0.693
λ =
t1
2
convert to
seconds
Divide λ by 3.7 x 1010 s-1 to get the activity in Curies.
Fraction of Nuclei Remaining and the
Elapsed Time
To Calculate the fraction of nuclei:
Nt
log
N0
=
-λt
2.303
=
-0.301 t
t1
2
To Calculate the elapsed time:
N0
1
t
t = 3.323
log
2
Nt
To Calculate the "Age" of a sample, Infer the fraction from
the Experimental Data and know the half-life or the activity.
Radiocarbon Dating
Based on the near constant levels of Carbon-14
in the Earth’s atmosphere formed by the
reaction: 14
14
1
1
7N
+
n
0
6C
+
H
1
Constant Carbon-14 levels maintained by:
Constant levels of nitrogen atoms in the
atmosphere as N2.
Constant levels of high energy neutrons from
the sun.
Radiocarbon Dating
Calculate the age of a Jaw bone whose activity is 4.5 dis/s
per gram of contained carbon if current activity levels are
15.3 dis/s per gram of contained carbon. The half-life of
Carbon-14 is 5730 years.
Infer the Carbon-14 fraction and calculate the elapsed time:
t = 3.323 t 1 log N0
2
Nt