Download Nuclear Chemistry I: Radioactivity Reading: Moore chapter 20

Nuclear Chemistry I: Radioactivity
Reading: Moore chapter 20, sections 20.1-20.4
Questions for Review and Thought: 11, 15, 17, 19, 23, 25, 29.
Key Concepts and Skills:
•
definition of radioactivity, activity, α-particles, β-particles, binding energy,
binding energy per nucleon, nucleon, curie, gamma radiation, positron, electron
capture
•
Write a balanced equation for a nuclear reaction; decide whether a particular
radioactive isotope will decay by α, β or positron emission or by electron capture;
Calculate nuclear binding energy for a particular isotope; calculate half-life from
activity; use half-life to find the time required for an isotope to decay to a
particular activity.
Lecture Topics:
I. Nuclear Chemistry - definitions
Nuclear Chemistry is closely connected with the study of radioactivity and radioactive
elements.
Radioactivity is defined as the spontaneous emission of energy and/or subatomic
particles by unstable atomic nuclei. It may refer to the energy or particles emitted.
Note: The basic building blocks of the nucleus, neutrons and protons, are referred to as
nucleons; forms of an element with the same atomic number and different mass numbers
are isotopes. Some isotopes are stable; some isotopes are radioactive: Ex. 11H (stable),
2
3
1 H (stable); 1 H (radioactive)
• 3 types of radiation are typically emitted from unstable nuclei
1.) α-radiation – positively charged particles known as helium nuclei, 24He2+; αradiation has very little penetrating power and is thus readily absorbed
2.) β-radiation – negatively charged particles – electrons, -10e (or β−), which have
more penetrating power than α-particles, and are less readily absorbed.
3.) γ (gamma) radiation is electromagnetic radiation (not particles) and is the most
penetrating form of atomic emission, consisting of highly energetic “photons”.
Gamma radiation carries no charge and is unaffected in its path by an electric
field.
Note that Radioactivity is a natural change of a radioactive isotope of one element into
an isotope of a different element.
Examples:
parent isotope
daughter isotope
226
4
Ra ==> 2 He + 86222Rn
88
mass #
226 ==> 4 + 222
atomic #
88
==> 2 + 86
• A nuclear reaction always results in a change in atomic number and frequently a change
in mass number
• The sum of the mass numbers of reacting nuclei must equal the sum of the mass
numbers of the nuclei/particles produced
• The sum of the atomic numbers of the products must equal the sum of the atomic
numbers of the reactants
II.
Features of Radioactive Decay
•For α-particle emission from an isotope, the atomic number decreases by 2 units and the
234
mass number decreases by 4 units:
U ==> 24He + 90230 Th
92
•For β-particle ejection from an isotope, the new element formed has an atomic number
one unit greater than that of the decaying nucleus:
239
U ==> -10e + 93239 Np
92
How does the atomic number increase by the mass number remain the same?
1
0
1
Neutron decay:
(+11p= proton; 1 0n=neutron)
0n ==> -1 e + +1 p
•β-radiation can also take the form of positron emission, where a positron is β+ or +10e.
207
Po ==> +10e + 83207Bi
84
This process is the opposite of β−-decay, because positron ejection leads to a decrease in
atomic number:
1
0
1
Proton decay:
since a neutron is created, the mass
+1 p ==> +1 e + 0n
number of the daughter isotope equals that of the parent isotope in positron emission.
• Atomic number also decreases by one unit when an inner-shell electron is captured by a
7
0
nucleus:
==> 37Li
4 Be + -1 e
electron capture converts a proton to a neutron: +11p + -10e ==> 01n
III.
Radioactive Series
A series of nuclear reactions in which a radioactive isotope undergoes successive
nuclear transformations resulting ultimately in a stable, nonradioactive isotope is a
radioactive series. Example: Uranium-238 series:
238
U ==> 24He + 90234 Th
92
234
Th ==> -10e + 91234 Pa
90
234
Pa ==> -10e + 92234U
91
234
U ==> 24He + 90230 Th
92
10 more steps:
210
Po ==> 24He + 82206Pb
84
IV.
Nuclear Stability
There are certain stable proton/neutron configurations in nuclei. In a graph of number
of neutrons N (x-axis) vs. number of protons Z (y-axis), the line of maximum nuclear
stability has a slope corresponding to a 1:1 proton:neutron ratio for the lightest nuclei
(==> 20Ca). Examples: 24He, 714N, 2040Ca.
For heavier nuclei, the slope gradually falls away toward a value of 1:1.6
(Z:N)(e.g.:83209Bi,80201Hg). The position of a given unstable nucleus with respect to this
line determines the type of process by which it is likely to decay.
Beyond Bismuth all isotopes are unstable and radioactive, and the rate of disintegration
becomes greater the heavier the nucleus.
Basis of nuclear stability: more neutrons are needed for stability in heavier elements: the
coulombic repulsive charge between protons is moderated in the presence of neutrons.
V.
Nuclear instability
Unstable nuclear arrangements arise from three general sets of circumstances, and the
instability tends to be self-correcting through a number of decay processes.
1. Excessively large numbers of protons and neutrons (elements heavier then
Bi). Nature’s solution: lose an α-particle. The driving force for this
process is the high stability of the α-particle: 92235U ==> 24He + 90231 Th
2. Excess of neutrons over protons (to the right of the line of stability): decay
by β− particle emission corrects this problem by converting a neutron to a
proton and an electron: 93239Np==> -10e + 94239Pu
3. Excess of protons over neutrons (to the left of the line of stability):
unstable nuclei correct this situation either positron emission or electron
13
0
13
79
0
79
capture:
7 N ==> +1 e + 6 C;
36 Kr + -1 e ==> 35 Br
•Given an unstable isotope, be able to write an equation for its probably mode of decay.
VI.
Mass Defect and Binding energy
Nuclear binding energy, Eb, is a measure of the force holding the nucleus together;
It must be a strong attractive force in order to overcome proton-proton coulombic
repulsion. A nucleus can contain up to 83 protons until it becomes unstable.
1
+1
p + 01n ==> 12H ΔE= -2x108kJ;
Eb = -ΔE = 2x108kJ
The mass of a nucleus is less than the sum of the masses of its compoenent neutrons and
protons; this missing mass is converted to energy: ΔE=(Δm)c2
Mass +11p = 1.007825µ; mass 01n = 1.008665µ mass 12H= 2.01410µ; Δm= -0.00239µ
ΔE= (-2.39x10-6kg)(3x108m/s)2=-2x108kJ
For helium: 2+11p + 2 01n ==> 24He Eb = 2.73x109 kJ/mol
Eb/mol nucleons = 2.73x109 kJ/4 mol nucleons = 6.83 x108 kJ/mol nucleons
For lithium: 3+11p + 3 01n ==> 36Li Eb/mol nucleons=5.15x108kJ/mol nucleons
•The greater the binding energy per nucleon, the greater is the stability of the nucleus
•The maximum stability is achieved in the iron nucleus: 2656Fe.
•All elements heavier than iron may split, or fusion, to give more stable nuclei with
atomic numbers nearer to iron, releasing energy.
•Lighter nuclei than iron may combine and undergo fusion exothermically to form
heavier nuclei
•Iron is the thermodynamically most stable element in the universe.
VII. Rates of radioactive decay
Radioactive decay is a first-order process; half-life expresses the instability of a
radioactive isotope.
C ==> D + particle (or γ-ray)
Remember: lnCt – lnCo = -kt;
for Ct= 1/2C0
t1/2=ln2/k=0.693/k
Note that half-life, which is defined as the time it takes for 1/2 of a radioactive sample to
decay to another isotope, is the same no matter the initial concentration.
Radioactive decay follows an exponential decay pattern:
Example: if a sample emits 2000 β- particles per minute, how long will it take to reduce
to 125 β- particles per minute? Given: 3890Sr ==> -10e + 3990Y
t1/2=29 years!
Answer: 4 half-lives or 116 years.
•Some half-lives are on the order of 106 years; how does one measure rates of decay?
Activity A is defined as the number of disintegrations per unit time:
A= k N
K is the first order rate constant; N is the number of radioactive atoms present.
Since At/Ao = kNt/kN0, then
At/A0=Nt/No
At/A0 or Nt/No expresses the fraction of atoms remaining after time t. Note that activity is
measured by a Geiger counter.
•The unit of activity A is the Curie: 1 Cu=3.7x1010 disintegrations/second.
• Since rate=activity, ln A = -kt + lnA0; lnA/A0 =-kt; ln N/N0=-kt
• By this method, k can be calculated from either A and A0 and time or N, No and time.
Example: Radioactive waste with a half-life of 200 years is stored in underground tanks.
What time is required to reduced an activity of 6.5x1012 disintegrations/minute to
3.0 x10-3 disintegrations/minute? k=0.693/t1/2 = 0.693/200y = .0034y-1
lnA/Ao=-kt = ln 3x10-3/6.5x1012 = kt; t=1.04x104 years
Problem set #15.
1. Given that the stable isotope of sodium is 1123Na, what kind of radioactivity would
you expect for 1122Na and 1124Na respectively, and why? Write equations to show
the decay processes.
2. Compute the total binding energy and the binding energy per nucleon: 12H, 612C,
56
26 Fe.
3. The nucleus 92235U is unstable and decays by sequentially emitting alpha (α) and
beta (β−) particles in the following order: α β α β α α α α β β α
Write the series of nuclei (isotopes) that are produced by the disintegration
process.
4. (a) Yttrium-90 and copper-66 are both β−-emitters. Identify both daughter isotopes
(b) Plutonium-236 and protactinium-226 are α-emitters. Identify both daughter
isotopes.
5. Calculate the number of disintegrations per second for a gram of 88226Ra. The halflife for the radioisotope is 1620 years.
6. A medicinally important isotope of iodine, 53131I, has a radioactive half-life of
193.2 hours, decaying to a stable xenon isotope.
(a) Write the nuclear reaction of the indicated decay process
(b) If the iodine isotope has an initial decay rate of 1500 counts per minute,
what would be the rate after 24 hours have elapsed?