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Chapter 2 Nuclear Transformations

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2.1 RADIOACTIVITYFirst discovered by Becquerel in 1896, radioactivity is a phenomenon in which radiation (,, or ) is given off by the nuclei of the elements. Pierre and Marie Curie discovered radium and polonium in 1898.

Henri Becquerel (1852-1908)

                 

The Nobel Prize in Physics 1903

Pierre Curie (1859-1906)

Marie Curie (1867-1934)

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Nucleons (protons, neutrons) in a nucleus possess kinetic energy. In a stable nucleus, this energy is insufficient to penetrate the potential barrier. In a radioactive nucleus, it has excess energy that is constantly redistributed among the nucleons by mutual collisions.

As a matter of probability, one of the particles may gain enough energy to escape from the nucleus, leaving the nucleus in a lower energy state. The emission of a particle may still leave the nucleus in an excited state, further emissions follow until the the nucleus is stable (ground state).

2.1 RADIOACTIVITY (cont’d)

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2.1 RADIOACTIVITY (cont’d)

radium source

magnetic field applied perpendicular to the paper

(++)

(-)

A=4

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2.2 DECAY CONSTANT

In a large collection of atoms, the number of atoms that will decay (or disintegrate) per unit time is proportional to the number of radioactive atoms present. is the decay constant.

Nt

N = - N

N = N0e-t

d Nd t

= - N

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2.3 ACTIVITY

The rate of decay dN/dt is called activity.

A = A0e-t

A = - N

The unit of activity is the curie (Ci), defined as:

1 Ci = 3.7 1010 disintegration/sec (dps)

Similarly, 1 mCi = 3.7 107 dps, and 1 Ci = 3.7 104 dps.

The SI unit is becquerel (Bq):

1 Bq = 1 dps = 2.70 10-11 Ci.

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2.4 THE HALF-LIFE and THE MEAN LIFE

The half-life (T1/2) is the time required for the activity (or the number of radioactive atoms) to decay to half the initial value.

N/N0 = A/A0 = ½ = e-T1/2

T1/2 =

ln 2

0.693=

The mean life or average life, Ta, is defined as:

Ta = 1

= 1.44 T1/2

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0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6

Time (T1/2 Units)

Act

ivity

Rem

aini

ng (

%) A = ½n

1

10

100

0 1 2 3 4 5 6Time (T1/2 Units)

ln(A) = -n ln(2) = -0.693 n

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Example 1

(a) Calculate the number of atoms in 1 gram of 226Ra.

Number of atoms/g = NA/AW = 6.021023/226 = 2.661021

(b) What is the activity of 1 gram of 226Ra (T1/2 = 1622 years)

A = N

= 0.693/ T1/2 = 0.693/(1622y 365d/y 86400sec/d)

= 1.356 10-11/sec

A = 2.661021 1.356 10-11 dps/g

= 3.61 1010 dps/g

= 0.975 Ci/g (specific activity)

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Example 2

(a) Calculate the decay constant for 60Co (T1/2 = 5.26 years) in units of month-1.

= 0.693/ T1/2

T1/2 = 5.26 years = 63.12 months

= 0.693/63.12 = 1.0979 10-2 /month

(b) What will be the activity of a 5,000 Ci 60Co after 4 years

A = A0e-t

= 5000 e -1.0979 10-2 48

= 2952 Ci

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Example 3

When will 5 mCi of 131I (T1/2 = 8.05 days) and 2 mCi of 32P (T1/2 = 14.3 days) have equal activities?

For 131I : A0 = 5 mCi, = 0.693/8.05 = 8.609 10-2 /day

For 32P : A0 = 2 mCi, = 0.693/14.3 = 4.846 10-2 /day

5 e –8.609 10-2 t = 2 e –4.846 10-2 t

ln 5 – 8.609 10-2 t = ln 2 – 4.846 10-2 t

t = 24.34 days

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2.5 RADIOACTIVE SERIES

Naturally occurred elements (Z = 1 to 92), artificial elements (Z = 93 to 103).

Radioactive elements tend to have higher Z.

Naturally occurred radioactive elements grouped into 3 series:

Uranium series: 238U (T1/2 = 4.51109 years) ,,() 206Pb

Actinium series: 235U (T1/2 = 7.13108 years) ,,() 207Pb

Thorium series: 232Th (T1/2 = 1.391010 years) ,,() 208Pb

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2.6 RADIOACTIVE EQUILIBRIUM

If the half-life of the parent > the half-life of the daughter, then after a certain period of time, a condition of equilibrium is achieved: A2/A1 = constant

The apparent decay rate of the daughter is then governed by the half-life of the parent.

parent nuclide daughter nuclide(radioactive) (radioactive)

decay, 1

teAA

NNdt

dN

Ndt

dN

12112

212

22112

111

decay, 2

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2.6 RADIOACTIVE EQUILIBRIUM (cont’d)

1.0

0 20 40 60 80 100 120

Time (hours)

0.5

0.1

99Mo

99mTc

Transient equilibrium:

T1/2 of the parent is not much longer than the T1/2 of the daughter.

99Mo: T1/2 = 67 h

99mTc: T1/2 = 6 h

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2.6 RADIOACTIVE EQUILIBRIUM

0 5 10 15 20 25 30

Time (days)

1.0

0.5

0.1

Secular equilibrium:

T1/2 of the parent is much longer than the T1/2 of the daughter.

226Ra: T1/2 = 1622 years

222Rn: T1/2 = 3.8 days

222Rn

226Ra

A1 = A2

1N1 = 2N2

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2.7 MODES OF RADIOACTIVE DECAY

X Y + He + QAZ

A-4Z-2

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-particle decay: (nuclides with too many protons)

• Radioactive nuclides with very high atomic numbers (greater than 82) decay most frequently with the emission of an a particle

Ra Rn + He + 4.87 MeV22688

22286

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Q appears almost entirely as kinetic energy of the -particle, because Y is much heavier than the -particle.

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P S + + + 1.7 MeV3215

3216

0-1

T1/2

14.3 days

Eavg = 0.69 MeV ~ 1/3 Emax

Emax = 1.71 MeV

2.7 MODES OF RADIOACTIVE DECAY (cont’d)

-particle decay:

X Y + + + QAZ

AZ+1

0-1Negatron emission:

(nuclides with too many neutrons)

-particles are emitted with a spectrum of energies.

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2.7 MODES OF RADIOACTIVE DECAY (cont’d)

X Y + + + QAZ

AZ-1

0+1

Na Ne + + + 1.82 MeV2211

2210

0+1

T1/2

2.60 years

Positron emission:(nuclides with too few neutrons)

Energy level diagram for the positron decay of to

EC(10%)

+(90%),Emax= 0.54 MeV

+(0.05%),Emax=1.83 MeV

Na2211

Ne2210

T1/2 = 2.60 y

(1.27 MeV)

(1.02 MeV)

Na2211 Ne22

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2.7 MODES OF RADIOACTIVE DECAY (cont’d)Electron capture: one of the orbital electrons is captured by the nucleus (when the nucleus has too few neutrons).

p + e n + 11

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0-1

X + Y + + QAZ

AZ-1

0-1

Most likely a K-shell electron is captured, called K capture.

Outer-shell electron falls into the (inner-shell) hole created by the captured electron, producing characteristic x-rays,

which may itself be absorbed and ejects an Auger electron.

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2.7 MODES OF RADIOACTIVE DECAY (cont’d)

Isomeric transition: sometimes, the excited state of the daughter nucleus persists for an appreciable time, called metastable state. This is the isomer of the final product nucleus.

In most radioactive transformations, the daughter nucleus loses the excess energy immediately in the forms of rays or by internal conversion.

In internal conversion, one of the orbital electrons is ejected from the atom, usually followed by characteristic x rays and auger electrons. (analogous to photo-electric effect)

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2.8 NUCLEAR REACTIONS

The ,p reaction: The bombardment of a nucleus by particles with the subsequent emission of protons.

X + He Y + H + QAZ

A+3Z+1

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Q>0: exoergic, energy is released

Q<0: endoergic, energy is absorbed (to be supplied by the bombarding particle in the form of kinetic energy).

Q is the difference in the masses of the initial & final particles.

N + He O + H – 1.19 MeV147

178

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AX (,p) A+3Y

BbaAorenergybBAa ),(

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2.8 NUCLEAR REACTIONS (cont’d)

The ,n reaction: The bombardment of a nucleus by particles with the subsequent emission of neutrons.

X + He Y + n + QAZ

A+3Z+2

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9Be (,n) 12C

Proton bombardment: proton being captured by the nucleus with the emission of rays.

X + p Y + QAZ

A+1Z+1

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7Li (p,) 8Be

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2.8 NUCLEAR REACTIONS (cont’d)

Deuteron bombardment: The bombardment of a nucleus by deuterons with the subsequent emission of neutrons or protons.

X (d,p) YAZ

A+1ZX (d,n) YA

ZA+1Z+1

H + Be B + n21

105

94

10

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2.8 NUCLEAR REACTIONS (cont’d)

neutron bombardment: neutrons are effective in producing nuclear reactions since they possess no electric charge. In particular, thermal neutrons (or slow neutrons, energy = 0.025 eV) are very effective.

(n,) reaction: B + n Li + He105

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10

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(n,) reaction: Co + n Co + 5927

6027

10

Co Ni + + 1 + 2 6027

6028

0-1

T1/2

5.26 years

(BNCT)

(Production of Co)60

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2.8 NUCLEAR REACTIONS (cont’d)

(n,p) reaction: N + n C + H147

146

10

11

C N + 146

147

0-1

T1/2

5700 years

(n,p) reaction:

P S + 3215

3216

0-1

T1/2

14.3 days

S + n P + H3216

3215

10

11

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2.8 NUCLEAR REACTIONS (cont’d)

Photo disintegration: Cu + Cu + n6329

6229

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fission:

U + n U Ba + Kr + 3 n + Q235

9210

23692

14156

9236

10

Q ~ 200 MeV

fusion:

H + H He + n + Q10

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21

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Q = 17.6 MeV

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2.9 ACTIVATION OF NUCLIDES

Radioactive elements can be made by various nuclear reactions.

The yield of a nuclear reaction depends on the number of bombarding particles, the number of target nuclei, and the probability of the nuclear reaction, called cross-section, given in units of barns (10-24 cm2).

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2.10 NUCLEAR REACTORS

In a nuclear reactor, self-sustaining chain reaction is achieved (called critical). High fluxes of thermal neutrons are produced (1010 to 1014 neutrons/sec/cm2).

Neutrons are slowed down by colliding with low-Z materials, called ‘moderator’, such as water, graphite, beryllium.

Radioisotopes such as 60Co are produced in nuclear reactors.