Week 5 - Nuclear Decay Flashcards
What is the definition of the röntgen and what was its limitation?
“ the electric charge freed by such radiation in a specified volume of air divided by the mass of that air”
Only measures air ionisation and not a direct measure of radiation absorption in other materials
This was replaced by the rad in 1953
What is the definition of the rad and what was it later replaced with?
“1 rad is equal to the dose causing 100ergs (1 ergs = 10-7 joules) of energy to be absorbed by 1g of matter”
Numerically equivalent SI unit is the centigray, cGy, used to report absorbed doses within radiotherapy (1975 onwards)
What is the definition of gray and how is it used?
“The absorption of 1 joule of radiation energy per kg of matter”
Unit: J/kg (m2/s-2)
Used as a unit of radiation absorbed dose that measures the energy deposited by ionising radiation in a unit mass of matter being irradiated.
Delivered dose: radiotherapy, food irradiation, radiation sterilisation
What is the Sievert and how is it used to measure health effects of radiation? What is equivalent dose, effective dose and committed dose?
“Represents the Stochastic health risk of ionising radiation i.e. probability of causing radiation-induced cancer & genetic damage”
Stochasticity refers to the modelling approach whereas randomness refers to the phenomena
Equivalent does, H - probability of cancer (specific organs, mSv)
Effective Dose - risk of external irradiation from sources outside the body ( whole body, mSv)
Committed Dose - risk of internal irradiation due to inhaled or ingested radioactive substances
Absorbed dose (Gy) x radiation weighting factor (W_R) x tissue weighting factor (W_T) = effective dose (sv)
1 sv = 5.5% probability of developing a fatal cancer
Explain the equation H = Q•D
H - Quantity dose equivalent (biological effect)
Unit - sv (J/kg)
D - absorbed dose (energy deposited in matter by ionising radiation per unit mass)
Unit - gray, Gy (J/kg) physical quantity
Q = dimensionless factor (function of linear energy transfer by the ICRU)
What is the becquerel Bq and how is it used?
“1Bq is the activity of a quantity of radioactive material in which one nucleus decays per second”
Unit - s-1
What are the most common decays around the line of stable elements?
Above the end point - alpha decays (heavy elements)
Above the line - beta + | EC
Below the line - beta minus
What is Q-Value equation for a beta minus decay if given the atomic masses?
Q (+ve) = [m(Z,A) - m(Z + 1,A)]c2
Where Q is the mass difference between the parent and the daughter atom
+ve Q means net mass is reduced and the lost mass is converted into energy
What are the equations of Q for positron and electron capture decay? What is the significant difference?
Q (EC) = [m(Z,A) - m(Z-1, A)]c2
Q (positron) = Q(EC) - 2me•c2
If Q => 2me•c2 (1.022MeV) both EC and positron decay are competitive processes (if less than only EC can occur)
It must be double the rest mass of a positron for beta plus decay to occur in order to be able to lose two electron-mass particles in the process, conserving the charge of the system.
Why is the energy levels of beta particles a spectrum when in the quantum world discrete energy levels are the rule?
Due to conservation of momentum, the KE of the daughter products (Q) will be very little in the main daughter isotope —hence a majority of the energy will be shared between the remaining products
Alpha and EC only have an alpha particle and neutrino remaining respectively, hence all the energy goes to them in discrete forms
I’m beta decay you have the beta particle and respective neutrino and hence the remaining energy is shared between those two particles, resulting in a spectrum of energy releases.
Most odd values of the nuclear mass number, A, yield only a single beta-stable nucleus e, whereas most even values of A yield two or more. Explain why using SEMF.
SEMF —> A’Z2 + B’Z + C’ (where A B C are constants)
Pairing term is in the C constant and is zero for odd A isobars. Odd-even is the only combination for Z and N and hence there is only only one parabola for which isobars will have one route to decay down (right via beta minus and vica versa)
Pairing term can be positive or negative for even isobars as Z and N can be even-even or odd-odd respectively. Hence you will have to parabolas separated by a distance of 2x the pairing term —> even-even is +ve and hence higher BE and stability and thus it’s parabola is lower —> meaning isobars can at the bottom of the odd-odd parabola can decay further via EC or another beta decay process to become more stable
Why do we discuss the rate of decay and what is the equation? What are the units?
Wave Nature of everything and the probabilistic nature of the quantum world means that we cannot say when a particular atom will decay but only predict the rate at which decays occur in a large sample.
The activity of a sample only depends on the number of atoms, N, in the sample and the decay constant, lambda. The decay constant describes the probability that an atom decays per unit time.
dN/dt = - lambda•N
Units: Bq (disintegration per 1 second)
What is secular Equilibrium in nuclear decay?
Def: “the quantity of a radioactive isotope remains constant because it’s production rate (due to decay of parent isotope) is equal to its decay rate”
• Can only occur if the half-life of the daughter radionuclide is much shorter than the half-life of the parent radionuclide.
•Assuming the initial concentration of radionuclide B is zero — full equilibrium takes several half-lives of radionuclide B to establish
How is the mean life, decay constant, and half life all connected?
Tau (mean) = 1/lambda
Tau1/2 (half-life) = ln(2)/lambda
How would write an expression for the total rate of decay for an isotope with multiple decay modes? Likewise for the mean life.
dN/dt = -(lambda1 + lambda2…+ lambda_n)•N
tau = 1 /(lambda1 + lambda2 + … + lambda_n)
