Atomic Structure and Decay Equations

Question 1

What is specific charge?

Answer 1

Specific charge is the ratio of the total charge of a particle to its mass.

Specific charge = charge/mass = Q/m

Its unit is coulombs per kilogram (C kg^-1)

Question 2

How do you calculate the specific charge of a nucleus or ion?

Answer 2

To calculate the specific charge of a nucleus:
Charge = no. protons x charge of protons (1.60 x 10^-19)
Mass = no. protons x mass of protons (1.673 x 10^-27) + no. neutrons x mass of neutrons (1.675 x 10^27)
Calculate charge/mass

To calculate the specific charge of an ion:
Charge = no. electrons added/removed x charge of electrons (1.60 x 10^-19)
Mass = no. protons x mass of protons (1.673 x 10^-27) + no. neutrons x mass of neutrons (1.675 x 10^27)
Calculate charge/mass

Question 3

What is an isotope?

Answer 3

Isotopes - nuclei with the same no. protons but different no. neutrons.

Question 4

What is strong nuclear force and why is it needed?

Answer 4

The strong nuclear force is a fundamental force that holds quarks together, therefore keeping the protons and neutrons bound in the nucleus. It acts between nucleons and overcomes the electrostatic repulsion between protons. Because the electrostatic repulsion between postively charged protons is much stronger than the gravitational attraction between nucleus, the strong nuclear force is needed to bind the nucleus together and maintain stability.

Question 5

How does the strength of the strong nuclear force vary with nuclear separation?

Answer 5

The strong nuclear force is highly repulsive at separations below 0.5 fm (femtometres = 1x10^-15 m)
It is very attractive up to a nuclear separation of 3.0 fm, with the max attraction at around 1.0 fm.
It quickly falls beyond this distance - very short range.

Question 6

How does the strong nuclear force compare with the repulsive electrostatic forces?

Answer 6

The electrostatic force between protons has a much larger range, but only becomes significant when proton separation is greater than 2.5 fm.
Electrostatic force is influenced by charge, unlike strong nuclear force, whose strength is the same for all types of nucleon.
The equilibrium position for protons, where electrostatic = strong nuclear, is around 0.7 fm.

Question 7

Alpha decay

Answer 7

Common in large nuclei with too many nucleons, e.g. uranium, radium - the nucleus is too big for the strong nuclear force to keep it stable.
Helium nucleus emitted - 2 protons, 2 neutrons
Short range - few cm in air

Question 8

Beta-minus decay

Answer 8

A neutron turns into a proton, emitting an electron and antineutrino.
Happens in nuclei with too many neutrons.

Question 9

Beta-plus decay

Answer 9

A proton turns into a neutron, emmitting a positron and neutrino.
Happens in nuclei with too many protons compared to neutrons

Question 10

Neutrino emission

Answer 10

Neutrino - subatomic particle with no charge and negligible mass.
Anti-neutrino - antiparticle of the neutrino.
Its existence was hypothesised to account for conservation of energy in beta decay.

Question 11

The Photon Model

Answer 11

Photon - a massless ‘packet’ or a ‘quantum’ of electromagnetic energy
Energy is not transferred continuously but as discrete packets of energy.

Question 12

Equation for the energy of a photon

Answer 12

E = hf; where E represents energy, h represents Planck’s constant, and f represents frequency.
This can also be rewritten using the wave-equation as E = hc/λ

Question 13

Properties of anti-particles

Answer 13

Corresponding matter and antimatter particles have opposite charges, the same mass, and the same rest-mass energy.

Question 14

Annihilation

Answer 14

Annihilation - the destruction of a particle-antiparticle pair when they collide and convert their mass into two gamma ray photons.
All the mass of the particle and antiparticle is converted back to energy.
The minimum energy of one photon after annihilation is the total rest mass energy of one of the particles:
E_min = hf_min = E_0

Question 15

Pair production

Answer 15

Pair production - the creation of a particle-antiparticle pair when a high-energy photon spontaneously converts its energy into mass.
This only happens if one photon has enough energy to produce the mass of both particles - only gamma ray photons can do this.
A third body, usually a nucleus, is needed to conserve momentum.
The minimum energy required for a photon to undergo pair production is equal to the total rest mass energy of the particles produced:
E_min = hf_min = 2E_0
To conserve momentum, the particle and antiparticle move apart in opposite directions