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15 - 1
RadioactivityRadioactivity
Radioactivity is the spontaneousdisintegration of an unstable nucleus.
All spontaneous nuclear reactions areexothermic.
Three types of radiation are alpha, beta, and
gamma.
15 - 2
Alpha RadiationAlpha Radiation
An alpha particle symbolized by α is thenucleus of a helium atom.
Another way to symbolize an alpha particle is
An example of alpha decay is given by theequation:
42
He .
Th23892U
23490 + 4
2He
15 - 3
During alpha emission, the atomic numberdecreases by 2 and the mass numberdecreases by 4.
Also indicated in the nuclear equation shown
below is a conservation of mass-energy andcharge.
Th23892U
23490 + 4
2He
Atomic number which is thenumber of protons.
Mass number which is the numberof nucleons.
15 - 4
Beta ParticlesBeta Particles
A beta particle symbolized by β is a highspeed electron.
Another way to symbolize an beta particle is
An example of beta decay is given by theequation:
e01 .
p11+ e0
110 n
15 - 5
During beta emission, the atomic numberincreases by 1 and the mass number
remainsthe same.
Also indicated in the nuclear equation shown
below is a conservation of mass-energy andcharge.
Atomic number which is thenumber of protons.
Mass number which is the numberof nucleons.
p11+ e0
110 n
15 - 6
Gamma RadiationGamma Radiation
A gamma particle symbolized by γ is a highenergy photon.
γ decay results from the redistribution ofcharge in the nucleus and accompanies
mostnuclear reactions.
Because neither the mass number nor theatomic number changes during γ decay it isusually omitted from nuclear equations.
15 - 7
A particular decay series starts with U-238followed by 4 emissions. The order of theemissions are an alpha, two beta, andanother alpha decay. What are you left
withafter the 4th decay?238
92U Th23490 + 4
2He
Th23490
U23492 + 0
-1e 2
U23492
Th23090
42
He +
15 - 8
Half-Life a Measure of Nuclear ActivityHalf-Life a Measure of Nuclear Activity
The half-life of a radioisotope (a radioactiveisotope) is the time necessary for one-half
ofthe atoms/nuclei to decay.
The rate of decay is independent of environmental conditions such as pressureand temperature.
Although the half-life remains the same, thenumber of nuclei decreases as a function oftime.
15 - 9
The rate of decay is given by
Rate = kN
where k is the rate or decay constant in units
of /s, /y, etc. and N is the number of atoms(nuclei) in the sample.
Rates are measure in unit of becquerel (Bq)which equals 1 disintegration/s.
A decay series come to an end when theproduct is stable (no longer radioactive).
15 - 10
Because the rate of decay is a first-orderkinetics process, the half-life is given by:
t1/2 =0.693
k
and the integrated rate law is given by:
ln NN0
= ln = -ktm0
m
where N and N0 are numbers of atoms ornuclei and m and m0 are masses in the sameunits.
15 - 11
Graph of Decaying Isotope vs TimeGraph of Decaying Isotope vs Time
The graph shown on the next slide is Mass of
Decaying Isotope vs Time.
The graph shows two important points:
Nuclear decay is an example of first-order kinetics which means the half-life remains constant which is 60 days.
As a radioactive substance decays, the amount of radiation decays as well.
15 - 12
Mass Of Decaying Isotope vs Time
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 100 200 300 400 500 600
Time (days)
Mas
s O
f Dec
ayin
g Is
otop
e (m
g)
1 half-life (60 days, 50.0 g)2 half-lives (120 days, 25 g)
Mass of Decaying Isotope vs Time
15 - 13
Bi-210 has a half-life of 5.0 days.Approximately would it take for 12.5% of a2.00 mg sample of this radioisotope to
decay?t1/2 = 5.0 dm0 = 2.00 mg
t1/2 =0.693
k =0.693
5.0k
ln = -ktm0
m
15 - 14
.
ln =0.875 × 2.00 mg
2.00 mg0.693
5.0- t
t = 0.96 days
15 - 15
Nuclear StabilityNuclear Stability
Atomic nuclei consist of positively chargedprotons and neutrons that are neutral.
According to the law of electrostatics,protons should repel each other and all
nucleishould disintegrate.
However, at very short distances ofapproximately 10-15 m, a strong nuclearforce (a strong attractive force) existsbetween nucleons (protons and neutrons).
15 - 16
The more protons that are packed in thesmall dense nucleus, the more neutrons areneeded to provide the “nuclear glue”.
The graph on the next slide shows that thelighter elements (up to about 20) haveapproximately equal numbers of protons
andneutrons.
However, the number of neutrons needed for
stability increases more rapidly than thenumber of protons.
15 - 17
Number Of Neutrons vs Number Of Protons
0
20
40
60
80
100
120
140
160
0 20 40 60 80 100
Number Of Protons (Z)
Nu
mb
er
Of
Ne
utr
on
s
(A -
Z)
Neutron Number vs Proton NumberNeutron Number vs Proton Number
1:1
Too many protons
Too many neutrons
50Sn (1.38:1)
6C (1:1)
82Pb (1.52:1)
15 - 18
The blue graph shows the nuclei that do not decay.
The stable nuclei are said to reside in the“belt of stability”.
As the number of protons in the nucleusincreases, the ratio of neutrons to protonsalso increases to provide nuclear stability.
15 - 19
Rules for Nuclear StabilityRules for Nuclear Stability
The neutron to proton ratio required for nuclear stability varies with atomic
number. For the lighter elements (up to about 20), the ratio is close to 1:1 as indicated by
both the red and blue graph segments.
As the atomic number increases beyond 20, the ratio of neutrons to protons increase as indicated by the blue graph segment.
15 - 20
All elements beyond Bi-83 are radioactive.
Nuclei with an even number of nucleons are more stable than those with an odd number of nucleons.
The unstable region resulting from the nucleus having too many neutrons
(above the blue segment) undergoes
spontaneous beta decay to become more stable.
15 - 21
The unstable region resulting from a nucleus with too many protons (below
the red segment) undergoes spontaneous positron decay or electron capture to become more stable.
For the lighter nuclei nuclei, positron emission is favored and for the heavier nuclei, electron capture is favored.
Electron capture occurs when a nucleus absorbs an innermost electron (n = 1) to form a neutron.
15 - 22
There are certain numbers of protons and neutrons that produce very stable nuclei.
These numbers are referred to magic numbers and are 2, 8, 20, 28, 50, 82, and 126.
p11+ e0
110 n
15 - 23
1) 93Li 6
3Li
At 20482Pb
or
63Li is more stable because as a light element,
a 1 proton : 1 neutron is required.
2) or 20985
is more stable because all elementswith Z > 83 are unstable.
20482Pb
Which pair of nuclei is more stable?
15 - 24
Nuclear Binding EnergyNuclear Binding Energy
It is always true that a nucleus has less mass
than the sum of its constituent particles.
This difference in mass is called the massdefect.
The mass defect can be used to calculate the
nuclear binding energy given by:
ΔE = Δmc2
15 - 25
where m is the mass in kilograms (kg), c isthe speed of light, 3.0 x 108m/s, and E is
thebinding energy in joules (J).
The greater the binding energy/nucleon, the
more stable the nucleus.
The energy equivalent of the mass defect istransformed into the kinetic energy of theparticles.
15 - 26
When a lithium nucleus collides with a proton,
two helium nuclei are formed each having amass of 4.0015 u. Using the giveninformation below, determine the amount
ofenergy released in this transmutation.
mLi = 7.0144 u 1 amu = 1u = 931 MeV
mp = 1.0073 umHe = 4.0015 u +Li7
3 + 11
H 42He 2 energy
15 - 27
Δm = mr – mp
Δm = 7.0144 u + 1.0073 u – 2 × 4.0015 u
Δm = 0.0187 u
E = Δm = 0.0187 u×931 MeV
1 u
E = 17.4 MeV