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## Nuclear fission and fusion

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### Nuclear fission and fusion

Types of decay process

Rates of decay

Nuclear stability

Energy changes

Fission and fusion

Forces at work in the nucleus- Electrostatic repulsion: pushes protons apart
- Strong nuclear force: pulls protons together
- Nuclear force is much shorter range: protons must be close together

Neutrons only experience the strong nuclear force- Proton pair experiences both forces
- Neutrons experience only the strong nuclear force
- But: neutrons alone are unstable

Neutrons act like nuclear glue- Helium nucleus contains 2 protons and 2 neutrons – increase attractive forces
- Overall nucleus is stable

As nuclear size increases, electrostatic repulsion builds up

- There are electrostatic repulsions between protons that don’t have attractive forces
- More neutrons required

Long range repulsive force with no compensation from attraction

Neutron to proton ratio increases with atomic number

Upper limit of stability

Upper limit to nuclear stability

- Beyond atomic number 83, all nuclei are unstable and decay via radioactivity
- Radioactive decay (Transmutation) – formation of new element

Mass number

Atomic number decreases

Alpha particle emitted

Atomic number

Odds and sods

- All elements have a radioactive isotope
- Only H has fewer neutrons than protons
- The neutron:proton ratio increases with Z
- All isotopes heavier than bismuth-209 are radioactive
- Most nonradioactive isotopes contain an even number of neutrons (207 out of 264). 156 have even protons and neutrons; 51 have even protons and odd neutrons; 4 have odd protons and neutrons

Nuclear processes relieve instability

- Chemical reactions involve electrons; nuclear reactions involve the nucleus
- Isotopes behave the same in chemical reactions but differently in nuclear ones
- Rate of nuclear process independent of T,P, catalyst
- Nuclear process independent of state of the atom – element, compound
- Energy changes are massive

Alpha particle emission

92 protons

146 neutrons

238 nucleons

2 protons

2 neutrons

4 nucleons

90 protons

144 neutrons

234 nucleons

Beta particle emission

53 protons

78 neutrons

131 nucleons

0 nucleons

-1 charge

54 protons

77 neutrons

131 nucleons

Other decay processes

- Positron emission: the conversion of a proton into a neutron plus positive electron
- Decrease in z with no decrease in m
- Electron capture: the capture of an electron by a proton to create a neutron
- Decrease in z with no decrease in m

19 protons

21 neutrons

40 nucleons

18 protons

22 neutrons

40 nucleons

0 nucleons

+1 charge

80 protons

117 neutrons

197 nucleons

0 nucleons

-1 charge

79 protons

118 neutrons

197 nucleons

Measuring decay

- Rates of radioactive decay vary enormously – from fractions of a second to billions of years
- The rate equation is the same first order process

Rate = k x N

Half-life measures rate of decay

- Concentration of nuclide is halved after the same time interval regardless of the initial amount – Half-life
- Can range from fractions of a second to millions of years

Mathematical jiggery pokery

- Calculating half life from decay rate

t = 0, N = No; t = t1/2, N = No/2

- Calculating residual amounts from half life

Magic numbers

- Certain numbers of protons and/or neutrons convey unusual stability on the nucleus

2, 8, 20, 28, 50, 82, 126

- There are ten isotopes of Sn (Z=50); but only two of In (Z=49) and Sb (Z=51)
- Magic numbers are associated with the nuclear structure, which is analogous to the electronic structure of atoms

Stability is not achieved in one step: products also decay

- Here atomic number actually increases, but serves to reduce the neutron:proton ratio
- Beta particle emission occurs with neutron-excess nuclei
- Alpha particle emission occurs with proton-heavy nuclei

Radioactive series are complex

The decay series from uranium-238 to lead-206. Each nuclide except for the last is radioactive and undergoes nuclear decay. The left-pointing, longer arrows (red) represent alpha emissions, and the right-pointing, shorter arrows (blue) represent beta emissions.

Energy changes and nuclear decay

- In principle there will be an energy associated with the binding of nuclear particles to form a nucleus
- Experimentally demanding!

Use Einstein’s relationship

E = mc2

- Consider the He nucleus:

Mass of individual particles = 4.03188 amu

Mass of He nucleus = 4.00150 amu

Mass loss = 0.03038 amu

- The “lost” mass is converted into energy – the binding energy, which is released during the nuclear process
- For the example above, the energy is 2.73 x 109 kJ/mol

Inter-changeability of mass and energy

- Loss in mass equals energy given out

E = mc2

- Tiny amount of matter produces masses of energy:

1 gram 1014 J

- Energy and mass are conserved, but can be inter-changed
- Binding energy per nucleon presents the total binding energy as calculated previously per nuclear particle
- Usually cited in eV, where 1 eV = 1.6x10-19J

He

Nucleon mass

U

H

Average mass per nucleon varies with atomic numberThe binding energy per nucleon for the most stable isotope of each naturally occurring element. Binding energy reaches a maximum of 8.79 MeV/nucleon at 56Fe. As a result, there is an increase in stability when much lighter elements fuse together to yield heavier elements up to 56Fe and when much heavier elements split apart to yield lighter elements down to 56Fe, as indicated by the arrows.

Mass changes in chemical reactions?

- Conservation of mass and energy means that energy changes in chemical processes involve concomitant changes in mass
- Magnitude is so small as to be undetectable
- A ΔH of -436 kJ/mol corresponds to a weight loss of 4.84 ng/mol

Fission and fusion: ways to harness nuclear energy

- Attempts to grow larger nuclei by bombardment with neutrons yielded smaller atoms instead.
- Distorting the nucleus causes the repulsive forces to overwhelm the attractive
- The foundation of nuclear energy and the atomic bomb

Nuclear fission

- Nuclear fission produces nuclei with lower nucleon mass
- One neutron produces three: the basis for a chain reaction – explosive potential
- Many fission pathways – 800 fission products from U-235

Nuclear fusion: opposite of fission

- Small nuclei fuse to yield larger ones
- Nuclear mass is lost
- Example is the deuterium – tritium reaction
- About 0.7 % of the mass is converted into energy

+E

The sun is a helium factory

- The sun’s energy derives from the fusion of hydrogen atoms to give helium

Fusion would be the holy grail if...

- The benefits:
- High energy output (10 x more output than fission)
- Clean products – no long-lived radioactive waste or toxic heavy metals
- The challenge:
- Providing enough energy to start the process – positive charges repel
- Reproduce the center of the sun in the lab
- Fusion is demonstrated but currently consumes rather than produces energy

Radioisotopes have wide range of uses

- H-3 Triggering nuclear weapons, luminous paints and gauges, biochemical tracer
- I-131 Thyroid treatment and medical imaging
- Co-60Food irradiation, industrial applications, radiotherapy
- Sr-90 Tracer in medical and agricultural studies
- U-235/238 Nuclear power generation, depleted U used in weapons and shielding
- Am-241 Thickness and distance gauges, smoke detectors

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