8. Radioactive Decays, etc. Flashcards
What makes most nuclei unstable?
Their BE/nucleon ratio for heavier elements
- Often energeticlaly more favourable to change to a different nucleus
What are the four decay processes
- Alpha decay
- Beta decay / electron capture
- Gamma decay
- Fission
State the properties of the decay constant, λ?
Decay constant - Probability per unit time that a nucleus decays
Activity, A = - dN(t) / dt = λ N(t)
What is the activity of a nucleus?
The number of decays in a sample per unit time
- Measured in Bq
If there are multiple decay channels, what is the decay constant, λ, equal to?
The sum of these probabilities
What is the half life of a nucleus equal to?
t_1/2 = ln(2) / λ
Where the lifetime, τ, is equal to 1/λ
When does a decay chain end?
When the particle has decayed into a stable state
What is the energy requirement for alpha decay to occur?
The BE(2, 4) > BE(Z, A) - BE(Z-2, A-4)
What is the energy released in an alpha decay equal to?
Q = (m_P - m_D - m_alpha) c^2 = E_D + E_alpha
- Mass of parent - mass of daughter - mass of alpha
- Assumes parent is at rest for KE of D and alpha
What are the three factors that the probability of an alpha decay depends on?
- Probability to find an alpha particle in the nucleus w(alpha)
- Frequency of collisions of the alpha with the barrier
- Transition probability of the alpha to tunnel through barrier
Describe the Energy-r graph for an alpha particle
- Alpha sits at some positive E before R_0
- Potential is flat negative then spikes to some positive value a bit before R_0 and exponentially decays after
- Alpha can tunnel due to its wavefunction existing on other side of the slope
How is the half life and the energy of the alpha particle related?
- Half life is a very strong function of the alpha particle energy
- Small changes in the alpha particle energy can have large effects on the half life
