E3 radioactive decay

radioactive decay

unstable nuclide undergoes spontaneous random process, emitting alpha/beta particles and/or gamma rays

stable vs unstable isotopes

stable: no. of neutrons = no. of protons. does not undergo radioactive decay. highest natural abundance among isotopes.

unified atomic mass unit

one twelfth of the rest mass of an unbound atom of carbon-12 in its nuclear and electronic ground state, having a value of 1.661×10^-27kg

1u = 931.5 MeVc^-2

interactions in nucleus of atom

• coulomb repulsion

  • protons all positive charge, repel each other

  • very significant because distance between protons is very small

• strong nuclear force

  • strong short-ranged force (around 10^-15m, only inside the nucleus)

  • nucleons (protons and neutrons) attract each other when near

• small nuclei usually equal no. of protons and neutrons but large nuclei need more neutrons to hold together: coulomb repulsion long range force vs strong nuclear force short range → therefore more neutrons needed for stability in large nuclei

  • balance of coulomb repulsion and nuclear force keep the nucleus together

  • if imbalanced (too many/few neutrons), nuclei unstable, undergo radioactive decay to become more stable (decays until it falls in the band of stability)

mass defect

difference between total mass of constituents and the mass of nucleus

mass of nucleus < mass of constituents because mass was lost as energy during formation of nucleus (binding energy)

binding energy

the amount of energy released when nucleus is assembled from its constituent nucleons OR amount of energy supplied to separate nucleus into its constituent nucleons.

• energy lost to form bond

• energy gained (work done) to overcome coulomb repulsion

• loss > gain → overall loss in energy (binding energy is lost)

• the higher the BE per nucleon, the more stable the nucleus

  • when A>60, BE per nucleon is about 8MeV

• fission/fusion is energetically feasible if BE per nucleon of products > reactants (ie products more stable)

spontaneous

radioactive decay is not triggered by external factors

random

radioactive decay is unpredictable, cannot determine exact moment of decay

why alpha/beta particles have circular motion when entering magnetic field?

• alpha and beta particles are charged, by FLHR will have circular motion

  • beta particle radius of motion smaller because less mass

• gamma ray has no charge (EM radiation) so will be in straight line

alpha particles

• has 2 protons, 2 neutrons, net charge of +2

• among emissions, alpha particle is the most stable, heaviest, least penetrating, highest ionising power

• alpha decay most likely because alpha particle is most stable

  • alpha decay: mass - 4, charge - 2

beta particles

• either electron (beta minus decay, charge -1. accompanied by anti-neutrino) or positron (beta positive decay, charge +1. accompanied by neutrino)

• are emitted with continuous range of energy, large variation in KE. unexpected as it deviates from laws of conservation of energy and momentum → difference in energy/momentum is due to emitting neutrino/antineutrino

beta minus decay

• when too many neutrons compared to protons

• neutron changes to proton + electron + anti-neutrino

neutrino

• explaining presence of neutrinos: electron emitted during beta decay expected to have KE of 156keV, but measured less (and it was a continuous range of energy, not discrete) → particle that is difficult to detect is carrying off the energy and momentum (therefore conversation of energy/momentum still applies, can have range of energies while maintaining discrete nuclear energy levels)

• neutrino has 0 charge, very small rest mass

beta positive decay

• when too many protons compared to neutrons

• nucleus emits positron and neutrino

gamma rays

• gamma rays are high-energy photons (EM waves)

• unstable nucleus decays from excited state to lower state → photons emitted

  • nucleus may already have undergone beta decay and lost positrons, but still too excited (eg ¹²C → ¹²C is the same just that lose energy through gamma radiation to become stable)

comparison of the 3 particles

• alpha decay most likely because alpha particle is most stable

• alpha particles are highly ionising due to their charge and relatively large mass. Due to its ionising ability, an alpha particle has very short range as it loses its energy rather rapidly.

• gamma rays are very weakly ionising because they are electromagnetic waves and carry no charge and no rest mass. Hence, they have the highest penetrating power.

antiparticle

same mass, different charge

position and electron

neutrino and anti-neutrino

geiger-muller counter

• used to measure radioactive decay near to a source

• setup

  • metal cylinder filled with low pressure gas

  • thin mica window: allows radiation to enter

  • high voltage connected across casing of tube and central electrode

• beta/gamma radiation ionises the gas → electrons/ions produced are drawn to electrodes → produces pulse of current → measure amount of radiation using counting circuit

  • alpha particles low penetration power, will be absorbed so not detected by GM counter

background radiation

• even when no source of radiation, will measure background radiation that’s produced naturally from air, rocks, soil etc

• background radiation can be measured over one-minute intervals

radioactive half life

time taken for half the number of unstable nuclei in a given sample to decay

decay constant λ

probability of decay of a nucleus per unit time → unit is s^-1 or year^-1

it is a constant that is unique to that particular nuclide

no. of decays in a short time: change in N = -λN X change in t

rate of decay (dN/dt) = -λN

law of radioactive decay

rate of decay decreases exponentially over time for a fixed sample,

no. of parent nuclei will decrease exponentially with time, rate of decrease depends on decay constant λ

N = N₀e^-λt

→ because the higher the initial no. of nuclei, the more decays there will be. but each decay decreases the no. of nuclei.

activity

(of a source) number of nuclei decaying per unit time → unit Bq

geiger-muller tube

• used to detect radiation

• setup

  • ionising chamber with low pressure gas

  • gas is kept inside by a thin mica sheet at opening → alpha particles can penetrate through

• radioactive particles enter → ionise gas → current flows between 2 electrodes

cloud chamber

• vapour turns into droplets of liquid when radioactive particle travels through it

• alpha particles form thickest lines, then beta particles

• gamma ray does not have enough ionising power to form any lines

applications

• use isotopes of oxygen sulfur and carbon to determine chemical composition of different materials and surfaces

• gamma-emitting tracers detect leaks in underground pipers

• carbon dating using carbon-14 to estimate age of specimen

convert energy in MeV to J

energy in MeV x 10^6 × 1.6×10^-19