PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

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PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

Nuclear size and Shape

Ch. 40

Z, the number of protons, the atomic number of the atom.

N, the number of neutrons.

A, the mass number of the nucleus, the total number of nucleons, A=N+Z.

• Nuclei exist bcse strong nuclear force overcomes electrostatic repulsion force over close distances inside nucleus

• Energetics & stability of nucleus depends on number of protons & electrons inside

From scattering experiments, nuclei are roughly spherical with radius proportional to number of nucleons A1/3

where R0=1.2-1.5 femtometres = 1.2-1.5x10-15m

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

Nuclear size and Shape

Ch. 40

• Volume is proportional to A, so density constant• Nucleus looks like a liquid drop• For light nuclei N~Z• For heavier nuclei the number of neutrons

increases• The extra uncharged neutrons act to stabilize

heavy nuclei from repulsive electrostatic forces

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

Nuclear density

Estimate the density of nuclear matter.

Density:

M = mass of proton/neutron = 1.67x10-27kg x AR0= 1.5x10-15m

Find density = 1.18x1017kg m-3

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

The radioactive decay process Ch. 40

-Decay: either a neutron turns into a proton, with emission of an electron (or proton turns into a neutron (

So A remains same, Z changes by +/-1

-Decay: excited nucleus decays into lower energy state via emission of a photon. A and Z constant

-Decay: tends to occur in heavier elements, which can become more stable by reducing their size

N and Z decrease by 2, A decreases by 4

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

Mass and binding energy

Ch. 40

• Binding energy per nucleon varies with mass number A

• For small A (<50)• Steady increase in number of

nearest neighbours as A increases• Therefore an increase in no. of

bonds per nucleon

• For medium A (>50) curve ~flat• Additional nucleons too far away• Nuclear forces saturate• Only nearest neighbours important

• For large A (>200)• Coulomb repulsion force becomes

large• Nucleus unstable, spontaneous

fission

• Fusion of nuclei to the left of Fe• Fission to the right

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

Mass and binding energy Ch. 40

• This plot of mass difference per nucleon v A is the negative of the binding energy curve

• The rest mass per nucleon for both very heavy (A>200) and very light (A<20) nuclides is more than for nuclides of intermediate mass

• Thus, energy is released when a very heavy nucleus breaks up into two lighter nuclei (fission)

• Or when two light nuclei fuse together to form a heavier nucleus (fusion)

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

Fission

• Very heavy nuclei can spontaneously break apart, placing limit on size of nucleus and number of possible elements

• Some heavy elements can be induced to fission by capture of a neutron

• Fission of 235U (right):• Nucleus excited by capture of neutron• Splits into two daughter nuclei & emits more

neutrons (avg 2.5)• Coulomb repulsion force drives fragments

apart• Thermal energy released (exothermic)• Self-sustaining reaction (chain reaction)

possible• Big bang with nasty isotopes• Or control in reactor by keeping number of

viable neutrons per reaction to 1

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

Fusion

• Two light nuclei fuse to form a heavier nucleus• Energy per unit mass > fission• Abundance of light elements holds great promise for producing power from

fusion• Fewer dangers than fission (chain reactions, nasty isotopes)• Bcse of coulomb repulsion, kinetic energies ~1MeV needed to get deuterium

and tritium close enough for nuclear forces to become effective & fusion to occur

• Scattering more likely• Particles must be heated to high enough temps (~108K) for fusion to occur as

a result of thermal collisions• Temps like this found in stars• At this temp, gas is a plasma of +ve ions and e-

• Confining plasma difficult• Done by star’s high gravity• Barely achieved in any fusion reactor to date