Each atom has a center called a nucleus that comprises protons and neutrons
Almost all of the mass of an atom is in the nucleus of neutrons and protons. They are surrounded by a cloud ☁️ of electrons ⚡.
If there is an excess of neutrons and protons, there will be nuclear instability. Will cause them to ∆ their state, e.g. neutron → proton; proton → neutron, etc.
When a nucleus is unstable, the nucleus will decay to a “lower state” and eject particles in the process to get to this lower energy state.
The Valley of Stability
Some nuclei are very stable (black line in the above plot) forming a kind of “valley” of stability in the center. On either side of this “valley” atoms may have too many or too few neutrons (compared to protons) making them unstable.
When we have too many neutrons (further right along the y-axis), we tend to have excess negative change. Atom will want to shed negative change to move back towards the black line, i.e. the valley of stability.
When we have too many protons (or too few neutrons), we’ll want to shed positive charge, which can be done in the form of positron emission (or in the form of alpha particles)
The further away from the black line, the more unstable the atom is. When unstable, they may be inclined to ∆ (e.g. by radioactive decay) to move to a more stable state in the valley.
This concept helps us predict which atoms are radioactive and how atoms decay.
Radioactive Decay
Radioactivity occurs when we have an instability in the nuclear structure of an atom. There’s several different ways in which this can happen:
Change in the number of protons at the center (i.e. change in Z)
Not only would we add protons or lose protons, but we’re also changing the chemical nature.
3 major processes that this can occur:
Alpha decay
Where a cluster of protons and neutrons (e.g. 24He) are expelled from the nucleus.
Common in very large atoms, such as uranium and plutonium.
Beta decay
Where either a proton sheds a positron (or a neutron sheds an electron), i.e. shed a little bit of charge either in the positive sense or in the negative sense → Z increases or decreases by 1, respectively, but A remains unchanged.
Does NOT change the number of nucleons, but it does change the amount of charge in the center of the nucleus.
Electron Capture
The innermost electron cloud ☁️ passes close by a large nucleus (“gets too close”) → the nucleus grabs an electron from the electron cloud ☁️ + a proton is changed to a neutron
Vacancy in innermost shell → shell of atom collapses → emits X-rays that can be detected
Isomeric transitions: No change in the number of protons, i.e. no change in Z
Gamma Decay or Gamma Ray Emission
We have an atom that maybe starts to raise its energy state → goes to a low energy state with no change in the number of nucleons or the number of protons at the center of it, but gives off energy and conserves energy → produces a gamma ray that then detected by the system
Most of these transitions are very fast (on the order of ps), but for 99mTc, it is a metastable state with a 6-hour half-life
Calculating the number of radioactive atoms in a sample
Is proportional to the number of atoms present
The change in the number is proportional to a constant (k, sometimes written as λ) times the number that’s present. When we integrate that we end up with the familiar exponential decay.
dtdN=−kN → Integration of this is ∫NdN=−k∫dt
N=N0⋅exp(−kt)
Example: We have a five millicary (mCi) dose of technitium that spilled on the floor carpet in the in a laboratory. And with a half life of 72 hours, how long must we wait to reach 1/1,000th of the activity remaining?
Dose=Dose0⋅exp(t1/2−t⋅ln(2))
t=ln(2)t1/2⋅ln(1,000) = 717 hours
Compton Scattering
The way that Compton scattering takes place is an incident photon scatters off an electron in the electron cloud and the photon heads off in a new direction and kicks out an electron into the media.
The amount of energy change is determined by the Compton formula.
The new energy is largely determined by the incident energy and the angle.
Higher incident energy → bigger energy change energy change
Higher unit angle → bigger energy change
Example: A technologist opens the 140 keV photon window to +/-14 keV (20%). What is the minimum single scattering angle that the energy window can reject (assume perfect energy resolution and mc2 = 511 keV?
