Nuclear Stability & Radioactive Decay

Notation for a nuclide (specific atom)

12C

6

•The left superscript is the mass number = number of protons + neutrons.

•The left subscript is the atomic number = number of protons.

Isotopes

• Atoms with identical atomic numbers but different mass numbers.

• (Two nuclides can have different atomic numbers and different mass numbers.)

Nuclear Stability

• Determined by neutron/proton ratio.– All nuclides with 84 or more protons are

unstable.– Light elements (up to atomic number 20): like

a neutron/proton ratio of 1.– For heavier elements, the neutron/proton ratio

required for stability > 1, and increases as atomic number increases.

– Of 2000 known nuclides, only 279 are stable with respect to radioactive decay.

Zone of Stability

Beta

decay

Positron emission or

electron capture

Alpha decay: heavy elements.

Radioactive Decay

• Represented by equations

• 14C 14N + 0e6 7 -1

Original nuclide Decay Mode

Decay Product

Decay Modes

• Alpha – common decay mode for heavy nuclides. Mass # by 4, atomic # by 2. Tends to slightly increase n/p ratio.

• Beta – mass # remains constant.– Net effect: neutron changed to proton. So this

is a likely decay mode for nuclides whose n/p ratio is too high – decreases n/p ratio.

Decay Modes

• Positron production: net effect: change a proton to a neutron.– Important decay mode for nuclides whose n/p

ratio is low – it increases the n/p ratio!

• Electron capture: inner-orbital electron is captured by the nucleus– Increases neutron-proton ratio

Decay series

• Some radioactive nuclides must go through several decay events to reach a stable (nonradioactive) state.

• 235U 207Pb

• 238U 206Pb

92 82

92 82

Kinetics of Radioactive Decay

• Can never predict exactly when a specific nuclide will decay.

• N = # of nuclides

• Rate = - (N/t) = kN

• i.e., the rate is directly proportional to the # of nuclides in the sample.

Rate = - (N/t) = kN

• ln(N/N0) = -kt

• N = # of nuclides remaining at time t• N0 = # of nuclides at t = 0.

Half-Life, t½

• Half-life of a sample = time required for the number of nuclides to reach half the original value, N0/2.

• t½ = 0.693/k

Nuclear Transformations

• Change of one nuclide into another• Target nucleus is bombarded by a “bullet”• “Bullet” may be a positive ion or a neutron

– Particle accelerators used for + ions– Positive ions must be accelerated to high KE

to overcome electrostatic repulsions• Cyclotron

– Neutrons quite different experimentally. Not repelled by target nuclei.

Transuranium Elements

• Elements 93 – 1** have been synthesized.

Uses of Radioisotopes

• Ratioactive Dating

• 14C 0e + 14N6 -1 7

Continuously produced

in atm by:

14N +

1n

14C +

1H

7 0 6 1

So, C-14 is incorporated into living plants.

As long as it is alive,

C-14 to C-12 ratio is constant.

When plant dies, 14

C/12

C ratio starts to

decrease.

t½ = 5730 yrs

Geologic History

• 238U 206Pb92 82

Medical Applications

• Radiotracers/Diagnosis– Radioactive nuclide whose pathway in an

organism can be traced by monitoring its radioactivity.

– I-131 thyroid– Th-201 heart

• Treatment

Thermodynamic Stability of Nucleus

• Mass of a nucleus is always less than the sum of the masses of the protons and neutrons that make up the nucleus.

• This difference is a measure of the binding energy

• Binding energy = energy released when nucleus is formed.

Chemical Potential Well

Pot

entia

l Ene

rgy

Separate Nucleons

Stable Nucleus

Green Arrow represents binding energy:

Energy RELEASED when nucleus is

formed.

Mass Defect for O-16

• 8p: (8 X 1.007276 amu) = 8.058208 amu• 8n: (8 X 1.008665 amu) = 8.06932 amu• 8e: (8 X 0.0005486 amu) = 0.004389 amu

• Total combined mass = 16.125789• Atomic mass of 0-16 = 15.994915 amu• m = 0.130874 amu• Use 1 amu = 1.66054 X 10-27 kg

Mass Defect for O-16

• m = 0.130874 amu• Use 1 amu = 1.66054 X 10-27 kg• m = 2.1732 X 10-28 kg• mc2 = E = 1.9559 X 10-11 kgm2s-2

• E = 1.9559 X 10-11 J per O-16 atom & 1.22 X 10-12 J per nucleon

• In kJ/mol: 7.4 X 108 kJ per nucleon per mol

Binding Energy/Nucleon vs. Mass #

Units of binding energy

• Chemists use kJ/(molnucleon)• Physics uses a different unit: Mev

Nuclear Fission

• Splitting a heavy nucleus into two smaller nuclei.

• U-235 and Pu-239 are fissionable fuels• Reaction initiated by a neutron

• Many, many possible products

Nuclear Fusion

• Two light nuclei combine to form a heavier, more stable nucleus.

• Occurs in the stars.• Sun: 73% H, 26% He, and 1% other• Protons fuse to form He

Sun

• 1H + 1H 2H + 0e + energy

• 1H + 2H 3He + energy

• Then • 3He + 3He 4He + 2 1H + energy

• 3He + 1H 4He + 0e + energy

1 1 1 1

1 1 2

2 2 2 1

2 1 2 1

Fusion vs. Fission as Energy Source

Nuclear vs. Ordinary Chemical & Physical Change

• Nuclear transformations involve much larger energy changes than ordinary chemical & physical changes– Orders of magnitude larger

Risks of radionuclides

• Somatic damage = damage to the organism itself, resulting in sickness or death

• Genetic damage = damage to genes