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.

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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

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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.

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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

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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

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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.

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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 +

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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.

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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).

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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.

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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.

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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

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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

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.

ln =0.875 × 2.00 mg

2.00 mg0.693

5.0- t

t = 0.96 days

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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).

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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.

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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)

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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.

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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.

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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.

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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.

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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

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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?

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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

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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.

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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

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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