Alpha Decay Flashcards
Why does alpha decay occur?
In heavy nuclei, the Coulomb repulsion between protons increases with increasing Z. The binding energy per nucleon for nucleons in the outer shells of these nuclei is less than the binding energy of an alpha particle and so it is energetically favourable for an alpha particle to be emitted.
What quantifies an unstable heavy nucleus?
A>190 and Z>80
Why is an alpha particle in particular emitted?
Alpha particles are doubly magic - they are more tightly bound than other (A>8) nuclei, so are energetically favourable.
What is the Q value for alpha decay? What does it’s value quantify?
Q = (M(X) - M(Y) - M(a))c2. It is the energy difference between initial and final states in the decay. A positive Q value means no extra energy is required - the process is spontaneous.
What is the assumption required for Q = T(Y) + T(a)?
The daughter nucleus is in its ground state.
What is the assumption required for Q = T(Y) + T(a)?
The daughter nucleus is in its ground state.
How can you use the Q value and the alpha’s kinetic energy to determine the mass of the daughter nucleus?
From momentum conservation, Q=T(a)*(1+M(a)/M(Y)) and hence the daughter nucleus’ mass can be determined.
Why might it be difficult to measure the daughter nucleus’ mass directly?
The daughter nucleus could also be unstable and have a very short half life.
What does the Geiger Nuttall plot show?
There is a strong correlation between the Q value and the half-life of the parent nucleus for nuclear isotopes.
What are the axes for the Geiger Nuttall plot?
The y axis is log(half life) and the x axis is Q (MeV).
What is the quantum mechanical explanation of alpha decay?
The alpha particle has a finite probability of tunnelling through the Coulomb barrier, even if the barrier height is greater than its energy.
What is the formula for the transition rate predicted from the QM alpha decay theory? Explain the terms.
\lambda = fPT where \lambda is the transition rate, f is the frequency of the alpha particle when it presents itself at the barrier, P is the preformation probability (usually taken to be 1) and T is the barrier penetration probability.
What is the underlying assumption of the QM description? Is it accurate?
That the alpha particle is preformed inside the daughter nucleus, and moves in a central potential due to the daughter nucleus. There is no experimental evidence to suggest that this is in fact the case, however we can say the alpha behaves as if it were preformed.
What are the 3 problems with the QM preformation model?
- the initial and final nuclear wavefunctions are ignored.
- we have ignored the angular momentum of the alpha particle.
- the nucleus is assumed to be spherical. In reality nuclei with A>230 are deformed.
How could studying alpha decay provide info on the excited states of nuclei?
Alpha decay can occur where the daughter nucleus is in an excited state. By measuring the alpha spectrum we can find out the distribution of these excited states (provided they have energies less than the ground state of the parent nucleus relative to the daughter’s ground state.
