ATOMIC AND NUCLEAR PHYSICS

Rutherford/Planetary/Nuclear Model of atom: the atom consists of a very tiny but very massive positive nucleus, surrounded by electrons that orbit the nucleus as result of electrostatic attraction between the electrons and the nucleus

evidence: Geiger and Marsden’s experiment:

• Alpha particles bombarded at a sheet of gold foil mostly passed through—atoms mostly consist of empty space.

• Particles that were deflected bounced straight back from the foil—the huge deflection of the alpha particles must have been caused by electrostatic repulsions between the positive alpha particles and a dense, positive nucleus.

limitations/problems: • Electrons are orbiting nucleus, therefore changing direction, and therefore accelerating

• According to Maxwell, any accelerating charge will generate an EM wave • This EM wave would be a release of energy and give off light at all sorts of wavelengths. • electron releasing energy should slow down and eventually spiral into the nucleus .

Bohr’s Model:

• Electrons orbit at specific energy levels (“discrete states”), called “stationary states.” – we say energy is quantized

• Electrons in these stationary states do not emit EM waves as they orbit.

• Photon must be first absorbed in order to be emitted. Absorbed photon has the energy equal to the difference between excited and ground state.

• Photon is emitted when an electron jumps from excited state to a lower energy state. Energy of that photon is equal to the energy difference between two states. Ephoton = ΔE, and frequency is given by Einstein’s relationship between energy and frequency of a photon:

E = hf h = Planck's constant = 6.627x10-34 Js

Modern approach - Schrodinger wave function:

• energy level model - give possible energies of electrons and probability to find electrons somewhere is given by wave function.

BTR

Problems with Bohr’s Model: It worked only for hydrogen atom

Continuous Spectrum (without prism white light)

• a spectrum having all wavelengths over a comparatively wide range • All possible frequencies of EM waves are present. • Generally, solids, liquids, or high pressured (dense) gases emit a continuous spectrum when heated.• Generally, strong interaction between molecules (spreading energy band)

Discrete/ Line spectrum - Evidence of electron energy levels

Pattern of distinct lines of color, corresponding to particular wavelengths.Generally, weak or no interaction between molecules (no spreading of energy band)

• Emission Spectrum

• Set of frequencies of the electromagnetic waves emitted by atoms of a particular element.

• A hot, low-density / low pressure gas (gas in the atomic state) produces an emission-line spectrum – energy only at specific λ.

• Absorption Spectrum

• Pattern of dark lines against a continuous spectrum background that results from the absorption of selected frequencies by an atom or molecule. • An absorption spectrum occurs when light passes through a cold, dilute gas and atoms in the gas absorb at characteristic frequencies; since the re-emitted light is unlikely to be emitted in the same direction as the absorbed photon, this gives rise to dark lines (absence of light) in the spectrum.

BTR

BTR

Nucleon: a proton or neutron.

Nuclide: A particular combination of protons and neutrons that form a nucleus. It is used to distinguish isotopes among nuclei.

XAZ

• X is chemical symbol of the element • Z is the atomic number = number of electrons or protons• A is the nucleon (mass) number = number of neutrons + protons • A – Z = number of neutrons

Isotopes: Nuclides contains the same number of protons but different number of neutrons. Isotopes are evidence for the existence of neutrons

Repulsive electromagnetic forces between the protons would cause the nucleus to disintegrate if it were the only force.

Strong nuclear force is an attractive force, which exists between all nucleons to hold them together. It is effective only over a very short range.

Weak nuclear force exists only in the nucleus and is responsible for the disintegration of a neutron into a proton and an electron in beta decay.

Nuclear Stability: depends on the neutron-proton ratio Nuclei are held together by a strong nuclear force, which counteracts the repulsive force among protons contained within it. As long as the attractive nuclear forces between all nucleons win over the repulsive Coulomb forces between the protons the nucleus is stable. It happens as long as the number of protons is not too high. Atomic nuclei are stable subject to the condition that they contain an adequate number of neutrons, in order to "dilute" the concentration of positive charges

♦ Small nuclei- tend to have equal number of neutrons and protons ♦ Large nuclei- tend to have more neutrons to counterbalance repulsive Coulomb force. The most massive isotope found in nature is uranium isotope U238

92 For more massive nuclei strong nuclear force can’t overcome electric

repulsion.

Radioactive Decay

Spontaneous decay of unstable nuclei. • process in which unstable nucleus loses energy by emitting “radiation” in form of particles or EM waves, resulting in transformation of parent nuclide into daughter nuclide. • three common radiations - alpha, beta, gamma • they differ in charge, ionization and penetration power.

Alpha decay:

• nucleus ejects an α particle, the atomic number is decreased by two and the atomic mass is decreased by four • charge is + 2e • the most ionizing and therefore the least penetrating (a few cm of air)• Governed by strong nuclear force = α decay occurs primarily among heavy elements because the nucleus has too many protons which cause excessive repulsion. In an attempt to reduce the repulsion, a helium nucleus is emitted. Mass of parent > mass of daughter + mass of alpha • difference = kinetic energy

Beta decay

● Beta particles are high energy electrons emmited from the nuclus• nucleus spontaneously emits beta particle and an antineutrino • In β− decay, the weak interaction converts a neutron into a proton while emitting an electron and an anti-neutrino:

• the most common decay occurs when the neutron to proton ratio is too great in the nucleus and causes instability

n01 → p  +  e− 1

011 (β− )+ν

• charge is – e • medium ionizing and therefore medium penetrating (a few mm of metal)

42He or 4

2aA A-4 4Z Z-2 2X Y +

A A 0Z Z+1 -1X Y + e +

Gamma Decay

• EM waves (high-energy photons) are emitted from a nucleus in an excited state dropping to a lower energy state (more stable)• charge is 0 • no ionizing and therefore highly penetrating (a few cm of lead or thick concrete can reasonably protect)

Biological effects of ionizing radiation

• Prompt effects: effects, including radiation sickness and radiation burns, seen immediately after large doses of radiation delivered over short periods of time. • Delayed effects: effects such as cataract formation and cancer induction that may appear months or years after a radiation exposure

Radioactive Decay is a random process on the atomic level, in that it is impossible to predict when a particular atom will decay, but given a large number of similar atoms, the decay rate, on average, is predictable. The rate of decay decreases exponentially with time.

Half – life T 1 /2 is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.

Activity (becquerel - Bq) of a radioactive sample is the average number of disintegrations per second.

Nuclear Reactions – A reaction that occurs whenever the number of protons or neutrons changes. Nuclear reactions include natural and artificial transmutation, fission, and fusion.

Transmutation – Change of one element into another.

In natural transmutations the nucleus decays spontaneously. There is only one nucleus that undergoes the transformation.

Artificial transmutation is induced by the bombardment of the nucleus by high-energy particles (Uranium atoms bombarded with neutrons to start fission reaction.)

Unified Atomic Mass Unit (u) is 1/12 of the mass of one atom of carbon-12 atom (6p+6n+6e)

• 1 u = 1.66056655 x 10-27 kg

• 1 u = 931.5 MeV c-2 due to relationship E = mc2

• 1 u of mass converts into 931.5 MeV

Mass Defect (∆m) is the difference between the total mass of all nucleons in the nucleus and the mass of the nucleus itself

∆m = Zmp + Nmn - Mnucleus (can be calculated in kg or u) . Equivalent to binding energy.

Binding Energy is the work/energy required to completely separate the nucleons of a nucleus / energy released when nucleons form a nucleus.

nuclear binding energy is actually energy that corresponds to mass defect

1. BE in MeV: • find mass defect in u and multiply it by 931.5 MeV

2. ME in J:

• BE = ∆m c2 (c = 3x108 m/s, ∆m = mass defect in kg)

In order to balance nuclear reaction the total mass/energy and total charge number of the reactants has to equal the total mass/energy and total charge number of the products.

Energy released/required in a nuclear reaction/artificial transmutation

Nuclear reactions A + B → C + D can either release energy or requires energy input.

• release energy: Energy will be released in nuclear reaction if Δm = LHS – RHS > 0 The total amount of energy released will be in the form of kinetic energy of products. If there was initial kinetic energy, that will be added up to released energy. energy released in nuclear reaction is found the same way as binding energy: first find mass difference and then equivalent energy

Δm in u, E = (Δm) x 931.5 (MeV) or Δm in kg, E = (Δm) c2 (J)

• energy input: if Δm = LHS – RHS < 0, reaction cannot be spontaneous. For example, some nuclei will decay only if energy is supplied to it - collision with fast moving α particle: α particle must have enough KE to make up for imbalance in masses, and to provide for kinetic energy of products.

Energy released in a decay - conservation of total energy (energy + mass). as always

Rn Ra 42

22286 226

88

M > m1 + m2 , but

total energy on the left = total energy on the right Mc2 = m1 c2 + m2 c2 + KE1 + KE2

• spontaneous decay: M > m1 + m2 → binding energy of the decaying nucleus < binding energies of the product nuclei. This is why radioactive decay happens with heavy elements lying to the right of maximum in the binding energy curve. Energy released is in the form of kinetic energy of the products.

Binding energy per nucleon: the work required to remove one nucleon from the nucleus; roughly the binding energy divided by the total number of nucleons in nucleus.

The binding energy of a nucleus is a measure of how stable nucleus is. Greater mass defect – higher binding energy – greater stability.

Most nuclei have a binding energy per nucleon of approximately 8 MeV.

Nuclear fission: process in which a large nucleus (A>200) splits up into two smaller nuclei, generally accompanied by the release of one or more neutrons and energy (as gamma rays and as kinetic energy of the fragments). Large amounts of energy produced, can be self-sustaining due to chain reactions. The total BE would increase which means that the daughters are more stable than parent. Spontaneous fission is very rare. Nuclear fusion: joining of two small nuclei into a bigger one, releasing great amounts of energy in the process. High temperatures are required to provide sufficient kinetic energy to approach each other, overcoming electrostatic repulsion.

When two small nuclei the product of fusion would have more BE per nucleon.The increases in binding energy per nucleon are much larger for fusion than for fission reactions, because the graph increases more steeply for small nuclei, so fusion gives out more energy per nucleon than fission.