Topic 7: Atomic, Nuclear, and Particle Physics

This paragraph contains no physics. I have not stuck to the syllabus’ subtopic labels. Their structure is, in my opinion, perhaps not the clearest. I have relabelled it in a way which I feel best conveys the physics.

7.1 – Atomic Physics

In the Bohr model of the atom, negatively charged electrons ‘orbit’ a positively charged nucleus. Depending on the radius of the ‘orbit’, the electron-nucleus system will have different amount of (electric potential) energy. However, not all radii are allowed. The ‘circumference of the orbit’ must be an integer multiple of the de-Broglie wavelength of the electron in order for it to interfere constructively with itself (this is analogous to standing waves). Since only certain discrete radii are allowed, the atom can only have certain discrete energy levels.

The lowest possible energy state is called the ground state. Higher energy states are called excited states.

When the atom transits from one energy level to another, a photon is either emitted or absorbed. This fulfills the conservation of energy. Consequently, if an atom from a lower energy state is excited to a higher energy state, it has to absorb a photon. Conversely, if an atom goes from a higher energy state to a lower energy state, it has to emit a photon. This photon will have an energy exactly equal to the magnitude of difference of the energies of the initial and final states, conserving energy.

In order to calculate the energy of the photon,

ΔEatom = Ephoton = hf

In words: the increase/decrease in energy of the atom is supplied/removed by the photon. Since a photon’s energy is directly proportional to its frequency, where the constant of proportionality is Planck’s constant, the frequency can thus be calculated.

When atoms are heated up (or subjected to a potential difference), the thermal (or electrical) energy excites them into higher energy states. These excited states then drop to a less energetic state, emitting a photon. This is a dynamic process, with atoms being thermally excited and losing their energy by emitting photons. Since only certain energy states are allowed, the corresponding transitions between the states are limited. Hence, the atoms can only emit photons with certain energies. In other words, the light emitted only has certain wavelengths. This is known as the emission spectrum, and is the physical principle behind neon lights.

When broadband (white) light passes through a material with such atoms, they excite the atoms; that is, they cause certain transitions to take place. The wavelength of light associated with the corresponding energy differences are absorbed. They are later re-emitted in all directions (isotropically). Hence, it appears as though certain wavelengths of light are ‘absorbed’.

Since atoms of different elements have different energy levels (due to different nuclear charges), the emission and absorption spectra enable us to determine which elements are present. In other words, these spectra are like the ‘fingerprints’ of these elements.

7.2 – Nuclear Physics

7.2.1 – Radioactive decay

There are four fundamental forces of nature. All forces we experience, all forces that exist, are manifestations of these four. In order of increasing strength, they are the gravitational force, the weak force , the electromagnetic force, and the strong force. The strong force is responsible for holding the nucleus together, preventing the tightly packed positively charged protons from flying apart. However, this force has a short range. Consequently, smaller nuclei are more stable than larger ones.

When nuclei are sufficiently large, they prefer to decay into more stable nuclei (refer to 7.2). There are several processes which facilitate this, three common ones are alpha, beta, and gamma decay.

When a nucleus undergoes alpha decay, it releases an alpha particle, which is really just a helium nucleus (2 protons and 2 neutrons). In case you are wondering why a helium nucleus and not some other nucleus, it is because the helium nucleus is small and very stable. In technical terms, it is said to be doubly magic, that is, it is more stable than similar nuclei – just as how noble gases are much more stable than elements which have a similar number of electrons.

There are two types of beta decay; the IB syllabus is mainly concerned with the one where an electron is emitted. A neutron in the nucleus decays into a proton, an electron, and an anti-neutrino. Since the proton usually stays in the nucleus and the anti-neutrino is difficult to detect, beta particles refer to the electrons which are emitted during beta decay.

neutron -> proton + electron + anti-neutrino

What about gamma decay? When a nucleus in an excited state reconfigures itself, it loses energy, and this energy is emitted in the form of a very high energy photon, a gamma ray. This process is similar to that of electrons losing energy and emitting a photon. However, since the energies in the nucleus are very high, the photon emitted has a much higher energy as well.

Radioactive decay is said to be random and spontaneous. Random means that it cannot be predicted when a particular nucleus will decay. Spontaneous means that the decay is not affected by the environment, that is, it is unaffected by temperature, pressure, and so on.

TODO: Ionizing power, tracks in magnetic field

The units of radioactive activity is the becquerel. A sample which has one decay event per second is said to have an activity of 1 becquerel.

Consider a sample of nucleus A decaying to nucleus B. Initially, there are quite a few of nucleus A. After some time, some of A has decayed to B. There are thus fewer A nuclei. Since the probability of any given nucleus decaying remains the same, having fewer nuclei means that the overall activity is less. Hence, one would expect the activity to drop with time. In more formal language, since the activity of a sample is directly proportional to the number of radioactive nuclei, and since activity is the rate of change number of radioactive nuclei, the activity of such a sample must decay exponentially over time.

The time required for a sample to lose half of its activity is known as the half life. Approaching this from another angle, the half life is also the time interval where a given radioactive nucleus has a 50% probability of decay.

7.2 – Nuclear reactions

Graph of binding energy per nucleon versus nucleon number.

The strong nuclear force has a short range. When the nucleus is big, some protons might be fairly far apart. A nucleon is unable to ‘feel’ the strong nuclear force from another nucleon which is on the other side of the nucleus. However, a proton feels the electrostatic repulsion from the other proton. This makes the nucleus less stable. Consequently, larger nuclei are less stable (nuclei larger than iron).

Nucleons on the surface of the nucleus have fewer neighbours than nucleons in the middle of the nucleus. Consequently, they feel less strong nuclear attraction from their neighbours. In other words, nuclei, like droplets of water, seek to minimise their surface area to volume ratio. For a certain increase in radius, the volume increases more than the surface area. Hence, larger nuclei are favourable (nuclei smaller than iron). This is similar to penguins huddling in a circle to stay warm; a smaller percentage of penguins will be cold if the group is bigger, hence bigger groups are preferred.

Nuclei are like groups of friends. If it’s too large, it will tend to fragment into smaller groups. If too small, adding more friends to the group will increase the happiness per person.

Mass defect.

Binding energy (separating nucleons to infinite distance apart from one another.

Unified atomic mass unit, definite to be 1/12 the mass of a neutral carbon-12 atom.

Transmutation – nuclear reactions where one element can be changed into another. Nuclear fission, where a larger nuclues splits into smaller nuclei. These smaller nuclei are known as the daughter nuclei. Uranium-235 and the role of the neutron in the chain reaction. Nuclear fusion, overcoming the Coloumb forces. Relate to binding energy graph.

7.3 – Particle Physics

7.3.1 Types of particles

Quarks. There are 6 of them. 3 of them have a charge of +2/3 (up, charm, top). The other 3 have a charge of -1/3 (down, strange, bottom). They are the constituent particles of protons (uud) and neutrons (udd), but not of electrons. Quark anti-particles are called ‘anti-quarks’. Lone quarks and anti-quarks do not exist; this is the principle of quark confinement.

Electrons are leptons. So are neutrinos. Specifically, there are three families of leptons: the electron and the electron neutrino, the muon and the muonic neutrino, the tauon and the tauonic neutrino. They all have their corresponding anti-particles.

Instead of thinking of forces acting by a field, one understand forces as the exchange of a type of particles. These are the force carriers. They are the photon (electromagnetic force), the W and Z bosons (weak force), and the gluon (strong force). Gravity is postulated to be mediated by the graviton, but that’s still an area of open research. The photon is massless and thus has a long range, whereas W, Z, and gluons have mass and thus have a short range. Mass is energy, hence a larger mass means they require more energy. Loosely speaking, the massive particles have more energy and are thus less stable, explaining their short range.

A hadron is a composite particle made up of quarks held together by the strong force.

  • A baryon is made of three quarks (qqq). For example, protons and neutrons.
  • A meson is made up of a quark and an antiquark (q qbar) (its own antiparticle)

Higgs boson and mass.

7.3.2 Conservation Laws

Conservation laws you should already be familiar with: mass-energy, charge, momentum.

Baryon number of a quark is 1/3, antiquark -1/3. Like charge and mass, baryon number must be conserved in reactions.

Strangeness = number of antistrange quarks – number of strange quarks. Strangeness is also conserved (actually, only for strong and EM interactions only, but not in syllabus)

Lepton number: 1 for all leptons (like electrons and neutrinos), -1 for all antileptons (like positrons and antineutrinos). Lepton number must be conserved. Also, the number of leptons in each generation must also be conserved.

Further information: Conservation laws are a consequence of symmetry, as explained by Noether’s Theorem. For example, the translational symmetry of the universe leads to the conservation of momentum.

7.3.3 Feynman Diagrams

Time ordering, scattering, beta decay, application of conservation laws

 

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