2 HRS SNM/VOICE CEU
 

A Tutorial by Stephen M. Karesh, PhD


Adapted for the Web by Stephen M. Karesh, PhD & Marsha Lipps CNMT


β- DECAY, β+ DECAY, ELECTRON CAPTURE, & ISOMERIC TRANSITION

DECAY BY NEGATRON EMISSION

If the n/p ratio is too large, a β- particle may be emitted to establish greater nuclear stability. β- emission is the only mode of decay that takes place in the neutron excessive region (see diagram below). The paradoxical emission of an electron from a nucleus containing only protons and neutrons may be explained by the following particle reaction:

The neutron is converted into a proton, which remains in the nucleus, increasing the Z number by 1 and decreasing the N number by 1. The electron is ejected along with a antineutrino, the two of which share E, the energy of transition. There is very little change in atomic mass since the mass of proton and neutron vary by less than 0.5% and the mass of the ejected electron is only 0.00005 of 1 atomic mass unit.

NEUTRON/PROTON RATIO GRAPH: β- DECAY

GENERIC EQUATION FOR β- DECAY

ß- DECAY OF P32 TO S32

N/P RATIOS FOR β- DECAY

CHANGE IN ATOMIC MASS

In the following equation, the A associated with X is very slightly greater than the A associated with Y. In fact, in all modes of decay, the atomic mass of the parent is greater than that of the daughter. Note that tthey appear to be the same if we look at the whole round numbers, but there will always be a difference in the 3rd or 4th decimal place.

DECAY SCHEME OF P32: DIRECT DECAY TO THE GROUND STATE, NO GAMMA RAYS EMITTED

DECAY SCHEME OF Au198:

Analogous to the earlier example of alpha decay, in the β- decay scheme, there are three possible routes of decay from parent to ground state of the daughter; the only mode of decay is alpha.

1. In Route 1, the decay is directly to the ground state. There is no excited or metastable state formed and no gamma rays are released.

2. In Route 2, there is decay by beta to a metastable state of the daughter, followed by emission of a gamma ray and transition to the ground state.

3. In Route 3, there is beta decay to a highly excited state of the daughter, followed by gamma ray emission either directly to the ground state or indirectly to the ground state through sequential emission of two separate gamma rays. Regardless of the route taken, the energy expended in transition from parent to daughter is a fixed amount.

COMPARISON OF ALPHA- AND BETA- DECAY SCHEMES

Alpha decay schemes and Beta decay schemes are mirror images of each other.

ß- PARTICLE ENERGY SHARING

The literature value for energy of beta emitters is Emax. The decay of P32to S32 is associated with a change in energy of 1.71 MeV. This energy is shared between the β- particle and a neutrino. This very strange particle has a mass of zero and a charge of zero, but possesses momentum and energy. Unlike α particles which are monoenergetic, ß- particles are emitted with a range of energies lying between 0 MeV and Emax for a particular isotope. This can be shown by means of a magnetic field which can be used to spread out ß- radiation from a particular source into a continuous spectrum. Diagram: sharing of energy between β- particle and neutrino.

POSITRON DECAY


NEUTRON/PROTON RATIO GRAPH

GENERIC EQUATION FOR β+ DECAY

Note that in positron decay, the Z number decreases by 1, N number increases by 1, and there is essentially no change in atomic mass.

EXAMPLE OF A β+ DECAY

N/P RATIOS FOR β+ DECAY

FATE OF POSITRONS IN MATTER

ELECTRON ENERGY EQUIVALENCE

By Einstein’s equation, the rest mass of an electron converted to pure energy is equivalent to 0.511 MeV. The 2 electrons have annihilated each other and produced energy in accordance with the Laws of Conservation of Matter and Energy

DECAY SCHEME FOR β+ EMITTING Zn65

Vertical bolded line represents the activation energy required for this mode of decay to take place. Energy equivalence is 1.02 MeV The angled bolded line represents the β+ portion of the decay scheme. Note that no excited states are associated with the β+ decay, although one is associated with the electron capture portion. β+ decay and Electron Capture are considered to be competing modes of decay.

DECAY BY ELECTRON CAPTURE

Electron capture often competes with positron emission. When the n/p ratio is low and sufficient energy is not available for positron emission, this ratio may be increased by the capture of an orbital electron by a proton in the nucleus. This process is also called K-capture since a K-shell electron is most often involved. With the loss of an electron in the K, L, or M shell, a vacancy exists, which is filled with an electron from a higher energy level. This is accompanied by emission of X-rays with energy levels characteristic of the daughter nuclide. It is by these characteristic X-rays that a nuclide decaying by EC can be detected.

PARTICLE REACTION FOR ELECTRON CAPTURE

GENERIC REACTION FOR ELECTRON CAPTURE

In Electron Capture Decay, the Z number decreases by 1, the N number increases by 1, and there is essentially no change in atomic mass.

EXAMPLE OF A β- DECAY

N/P RATIOS FOR EC DECAY


ELECTRON CAPTURE DECAY SCHEME: Zn65

ELECTRON CAPTURE DECAY SCHEME: Fe55

A: YES- even though gamma ray emission does not take place due to the absence of an excited state, characteristic X-rays are ALWAYS emitted in EC. If the energy is within the imageable energy range, an image can be formed.

 

ISOMERIC TRANSITION

When an excited state of a radionuclide decays to the de-excited state by gamma-ray emission, we call this transition "isomeric"; that is, there are no changes in A, Z, or N numbers, but only in nuclear energy levels. The parent and daughter nuclides are called nuclear isomers. The parent nuclide in Isomeric Transition is said to be METASTABLE, that is, it has a measurable half-life (longer than 1 µsec).

DECAY SCHEME: ISOMERIC TRANSITION

COMPOSITE DIAGRAM SHOWING ALL MODES OF DECAY

This diagram shows the correct angle for the lines in all modes of decay. In addition, the relationship of Z number of parent and daughter are shown.

CONCLUSIONS:

• When a nucleus is in a neutron excessive condition, the only mode of decay that can occur is β- emission.

• When a nucleus is in a neutron deficient condition, β- emission is not possible and the modes of decay that can occur are α emission, β+ emission and Electron Capture.

• Gamma ray emission can occur in every mode of decay as long as an excited or metastable state is formed

• In all modes of decay other than Isomeric Transition, there will be a significant change in the Z and N numbers and a very small change in the A number

• The lines drawn in a decay scheme are at an angle that reflects whether the Z number of the daughter is greater than, equal to, or less than the Z number of the parent

 

 

 

 

 

 

 
 

 


 

TUTORIAL NAVIGATION

 
    January 12, 2010