eV and J conversion: \(eV \times \text{(e elementary charge)} = J\)

planet evolution

protostar-> main sequence star, then two cases: 1. (if mass < 8 solar mass) red giant -> planetary nebula -> white dwarf 2. supergiant -> super nova -> blackhole/neutron star

Rutherford Experiment & Nuclear Physics Notes

Rutherford Experiment Conclusion

  • The centre of an atom (he called it the nucleus) must be positively charged in order to repel the positively charged alpha particles.

  • Alpha particles that pass close to a nucleus experience a strong electrostatic repulsive force, causing them to change direction.

Atomic Energy Levels

  • The emission, transmission and absorption of light are not continuous processes.

  • They consist of a very large number of separate events.

n levels of energy

  • （2 choose n）种

Photon Energy

The energy (E) carried by one photon of electromagnetic radiation depends only on its frequency (f):

\[E = hf\]

    1. is a fundamental constant controlling the properties of electromagnetic radiation.

Key Definitions

Isotopes

  • The nuclei of some atoms are unstable.

  • Spontaneous changes within an unstable nucleus can result in the emission of a particle and/or a high-energy photon.

  • This process is called radioactivity.

When particles are emitted:

  • The proton number of the atom may change

  • The atom becomes a different element

  • This is called transmutation or radioactive decay

Radioactivity

Spontaneous transmutation of an unstable nucleus

  • Individual nuclei decay randomly

  • No pattern or predictability

  • Each decay is spontaneous, without an obvious cause

However:

  • Large numbers of nuclei show statistical predictability

Transmutation

When a nuclide changes into a different element after emitting a particle.

Radioisotope / Radionuclide

An isotope / nuclide with an unstable nucleus which emits radiation.

Alpha Particles

  • Alpha particle = nucleus of helium (He)

Daughter Product

The resulting nuclide after a radionuclide (parent) emits a particle.

GM Tube (Geiger–Müller Tube) — Definition may appear in exam

  • A small amount of radioactive nuclide is contained in the source.

  • Radiation enters the GM tube through the end window.

  • The radiation ionizes the gas inside, causing a sudden burst of current.

  • These events are counted by an electronic counter / ratemeter.

Measurements:

  • Radioactive count

  • Count per second

(The tube and counter together are often called a Geiger counter.)

Background Radiation

Radiation from:

  • Radioactive materials in rocks, soil, and building materials

  • Cosmic radiation from space

  • Radiation escaping from artificial sources

Background Count

  • Measure of background radiation

Beta Particle

  • A high-speed electron released during beta-negative decay

  • OR a high-speed positron released during beta-positive decay

Penetrating Power

  • Depends on the ionizing power of the radiation

  • Radiation penetrates matter until it has lost nearly all its energy

  • Greater ionization per cm → less penetrating power

Ionizing Ability

  • Measure of how much ionization is caused when radiation passes through a material

Beta-Negative Decay

In an unstable nucleus:

  • A neutron converts into:

    • A proton

    • An electron

    • An antineutrino (\(\bar{\nu}\) )

Reaction:
\[ n \rightarrow p + e^- + \bar{\nu} \]

  • Antineutrino is an antiparticle (antimatter)

Properties of Nuclear Radiation (Summary)

Property Alpha (α) Beta⁻ (β⁻) Beta⁺ (β⁺) Gamma (γ)
Relative charge +2 −1 +1 0
Relative mass 4 1/1840 1/1840 0
Typical range in air 4 cm 30 cm Very short (annihilates) Very large
Composition Helium nucleus Electron Positron EM wave / photon
Typical speed ~10⁷ m/s ~2.5 × 10⁸ m/s (~0.9c) ~2.5 × 10⁸ m/s (~0.9c) 3.0 × 10⁸ m/s (=c)
Ionizing ability Very high Low Very low Very low
Absorbed by Thick paper 3 mm aluminium Quickly annihilates Intensity halved by ~2 cm lead

Activity of a Radioactive Source

Activity (A)

  • Number of nuclei decaying per second

  • Also called the rate of decay

Unit:

  • Becquerel (Bq)

  • 1 Bq = 1 decay per second

Notes:

  • 1 Bq is considered very low activity

  • Activity is proportional to the number of undecayed nuclei

Half-Life

  • Defined as the time taken for:

    • Half of the undecayed nuclei to decay

    • OR the activity (count rate) to halve

Symbol:
\[ T_{1/2} \]

Binding Energy

  • Energy released when a nucleus is formed from its constituent nucleons

  • Alternatively:

    • Energy required to completely separate the nucleons

Rest Mass

  • 和狭义相对论有关（考纲外）

Nuclear Fission

A nuclear reaction in which:

  • A massive nucleus splits into smaller, more stable nuclei

  • Total binding energy increases

  • Energy is released

used in nuclear reactor in nuclear electrc plant, therefore the waste is mainly fission induced products

Nuclear Fusion

A nuclear reaction in which:

  • Two low-mass nuclei combine

  • Form a more massive, more stable nucleus

  • Binding energy is greater than before

  • Energy is released

Mass Defect

  • Reduction in mass when separate nucleons combine to form a nucleus

  • Mass defect is equivalent to binding energy

Critical Mass

  • The minimum mass needed for a self-sustaining nuclear chain reaction

Moderator

  • Material used in a nuclear reactor

  • Slows down neutrons to low energies

  • Enables nuclear fission

Fundamental Forces

from strongest to weakest: 1. strong nuclear interaction force: holds neutrons and protons together in nucleus 2. electromagnetic force 3. weak nuclear interaction force: enable Beta decay 4. gravitational force