11. Nuclear Radiation Flashcards
What is Einstein’s Mass-Energy Equivalence Equation?
Applies whenever mass is truly converted into energy (nuclear fusion, fission, antimatter annihilation, particle creation)
Mass and energy are interchangeable
ΔE=Δmc^2
What is nuclear binding energy?
The energy equivalent to the mass deficit
When nucleons bind together to form an atomic nucleus
Experiments into nuclear structure have found that the total mass of a nucleus is less than the sum of the masses of its constituent nucleons
E.g a nucleus’ nucleons may sum to 13.0739u, but the total mass only be 12.9793u
This is called a mass deficit
The ‘lost’ mass is converted into energy (ΔE=Δmc^2) and is released when nucleons fuse to form a nucleus
What are constituents?
Nucleons (protons and neutrons)
Why are separated nucleons heavier in mass than a nucleus?
When the separated nucleons are bonded together to form a nucleus of an atom, some of the mass from these constituents (protons and neutrons) are interchanged for binding energy
Hence, mass of nucleus + binding energy = mass of separated nucleons
What is an atomic mass unit, u?
The change in mass when nucleons fuse is incredibly small
Hence we use atomic mass units to measure the change in mass
One atomic mass unit, u = 1/12th of the mass of a carbon-12 atom
u = 1.66x10^-27 kg
1u is actually slightly smaller than mass of 1 proton and neutron
- as scientists decided to take the mass of the atom carbon, which included the mass deficit due to binding energy present
What is the binding energy per nucleon?
The binding energy of a nucleus divided by the number of nucleons in the nucleus
This is the energy needed to remove one nucleon from the nucleus
A higher binding energy per nucleon indicates a higher stability since it requires more energy to pull the nucleus apart
What atom has the highest binding energy per nucleon?
Iron (Fe-56) has the highest binding energy per nucleon, which makes it the most stable of all the elements
What’s the binding energy per nucleon curve?
A curve with:
y-axis = Average binding energy per nucleon (MeV)
x-axis = Number of nucleons in nucleus
The curve spikes up very quickly, then becoming max around 56 (Fe) then slowly dropping
numbers lower than 56, the element undergo fusion
numbers higher than 56, the element undergo fission
What is nuclear fusion?
When 2 light nuclei (under 56) undergo fusion, they join together to make a single nucleus
Average binding energy per nucleon increases and nucleus loses more mass (due to the binding energy increase)
The nucleons need enough energy to become close enough to each other (~1fm, 1x10^-15m)
This overcomes the electrostatic repulsion force and the strong nuclear force takes over, fusing the nuclei together
The new nucleus also may come with a neutron that didn’t bine together
e.g deuterium + tritium -> helium + neutron + binding energy
What is nuclear fission?
Involves a heavy nucleus splitting into 2 lighter nuclei (+ usually some neutrons)
The average binding per nucleon increases
- seen on graph
Hence, leading to loss of mass
e.g U-235 + neutron -> U-236 -> Ba-144 + Kr-89 + 3 neutrons + binding energy in both Ba and Kr
What conditions are required for nuclear fusion to happen?
Fusion can only occur at extremely high temps (>1^7k)
- as a massive amount of energy is required to overcome the electrostatic force of repulsion between the nuclei’s so they can become close enough to each other (~1fm, 1x10^-15m) to fuse into one nucleus
this happens as protons are positive, repulsing each other
Also needs very high densities to ensure enough protons are colliding
Hence, also meaning very high pressure is needed
What force keeps the nucleons within the nucleus?
The strong nuclear force
- the strongest force in the universe
This force keeps the nucleons within the nucleus
The electrostatic force of repulsion
As the nucleus is positively charged, the protons will repulse one another
Overall, the electrostatic force of repulsion and the strong nuclear force act against each other, keeping the nucleus in equilibrium
What force is harder to overcome, strong nuclear force or electrostatic repulsion?
It depends on the distance
At long distances, electrostatic repulsion is stronger because the strong nuclear force has almost no effect beyond ~ 10^-15m
At short distances, the strong nuclear force dominates
What is a deuterium?
An isotope of hydrogen, containing 1 proton and one neutron
What is a tritium?
Another isotope of hydrogen, containing 1 proton and 2 neutrons
What is radiation?
When an unstable nucleus emits energy in the form of EM waves or subatomic particles in order to become more stable
measured in counts per second (Activity) in a unit called Becquerel (Bq)
- radioactive decay per second
Natural phenomenon, with radioactive elements having always existed on Earth and in outer space
However, human activity has added to the amount of radiation that humans are exposed to in various ways
What is background radiation?
Low levels of radiation from environmental sources, which are always present around us
Types:
Radon gas
- Uranium from rocks decays into radon gas, which is an alpha emitter
Rocks
- such as uranium and thorium
Cosmic rays
- high speed protons emitted from the sun collide with molecules in the air, this leads to the production of gamma radiation
Food and drink
- e.g potassium-40 in bananas
Carbon-14 in biological material
- living plants and animals
What are the different man-made sources of radiation?
Medical sources
- X-rays, CT scans, radioactive tracers, and radiation therapy
Nuclear waste
Nuclear fallout from nuclear weapons
Nuclear accidents
- e.g. Chernobyl
What are the 3 types of radiation?
Alpha, α
Beta, β
Gamma, γ
What properties is does an alpha, α particle consist of?
They are high energy particles made up of 2 protons and 2 neutrons (the same as a helium nucleus)
usually emitted from nuclei that are too large
Mass = 4u
Charge = +2
speed = 0.05c
Range = 2-10cm
Highly ionising
Absorbed by paper
What properties is does a beta, β particle consist of?
Beta minus decay, (0,-1)β particles are high energy electrons emitted from the nucleus
Beta plus decay, (0,1)β particles are high energy positrons emitted from the nucleus
emitted by nuclei that have too many neutrons
Mass = 0.0005u
Charge = ±1
c > speed > 0.99c
Range ~ 1m
Weakly ionising
Absorbed by aluminium foil (around 3mm)
What properties is does a gamma, γ ray consist of?
A gamma, (0,0)γ ray is a high energy EM wave
emitted by nuclei that need to lose some energy
Mass = 0
Charge = o
speed = c
Range = infinite: follows inverse square law
Very weakly ionising
Absorbed by several metres thick of concrete or inches of lead
What simple experiment can be used in order to identify the type of radiation?
Use a Geiger-Muller (GM) tube and count the background radiation
Place the source of radiation close to GM tube
Place sheet of paper in between
- if count significantly decreases = alpha radiation
Repeat steps above for aluminium foil and several inches of lead
What is the random nature of radioactive decay?
Radioactive decay is a random and spontaneous process that you cant predict
A given radioactive source will decay at an average rate
What is it meant by nuclear decay to be random?
Random means we cannot identify when atoms/ nucleus will decay
What is it meant by nuclear decay to be spontaneous?
Spontaneous means that the decay cannot be influenced by any external factors
What is the decay constant, λ?
The decay constant is the probability that the radioactive source decays every second
Activity = λN
dN/dt = -λN
Measured in s^-1
The decay constant stays constant, meaning radioactive decay isn’t influenced by any environmental factors
- meaning spontaneous
What is exponential decay?
A constant fractional change for a fixed time interval
What is the radioactive decay equation?
N=N(0)e^-λt
where N = number of nuclei at moment in time
N(0) = number of initial nuclei
As activity is directly proportional to the number of nuclei (A=λN) hence:
A=A(0)e^-λt
What is the half life, t(1/2)?
Half life is the time taken for half the number of nuclei in a sample to decay
This means when a time equal to the half-life has passed, the activity of the sample will also half, as A∝N
Hence,
N(0)/2=N(0)e^-λt(1/2)
1/2=e^-λt(1/2)
Ln(1/2)=-λt(1/2)
Ln2=λt(1/2)
λ=Ln2/t(1/2)
How can you plot N=N(0)e^-λt as a straight line?
N=N(0)e^-λt
N/N(0)=e^-λt
LnN - LnN(0) = -λt
LnN = -λt + LnN(0) is in the form y=mx+c
This gives a more accurate way of finding the decay constant, λ
As the gradient = -λ
