### FRCR Physics Notes

#### FRCR physics notes contents

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Radioactive decay generally involves the emission of a charged particle or the capture of an electron by the nucleus to form stable nuclides. The amount of decay = the radioactivity = the number of nuclear transformations per second.

## Nomenclature

 Nuclide nuclear species with specific number of neutrons and protons that exists in a defined nuclear energy state (e.g. 99mTc is a different nuclide to 99Tc) Radionuclide radioactive nuclide Metastable radionuclide a radionuclide that exists for a long time in a higher energy state before falling to ground state (e.g. 99mTc) Isomer the metastable version of a nuclide (isomer) of a nuclide e.g. 99mTc is an isomer of 99Tc Isotone nuclides with the same number of neutrons (isotone) but with a different number of protons Isotope nuclides with the same number of protons (isotope) but with a different number of neutrons

N.B. it is the number of protons that determines the element of an atom. You can change the number of neutrons (and, therefore, the mass number) and the atom will still be the same element.

## Nuclear stability

In the chapter on “Atomic structure” we covered nuclear stability and referred to the Segré chart. What the line of stability shows is that as the number of protons increases, the proportion of neutrons needed to keep the nucleus stable increases. When the nuclide doesn’t lie on the line of stability it becomes unstable and radioactive.

The decay model of nuclides above includes all nuclides; stable and radioactive. Nuclides in area A have too few neutrons, in area B have too few protons, and in area C are very heavy with excess protons and neutrons. The area the nuclide lies in determines the type of radioactivity the nuclide goes through to become stable and is discussed below.

The decay of a nuclide is exponential i.e. it theoretically never reaches zero.

The S.I. unit of radioactivity is the Becquerel (Bq):

1 Bq = 1 transformation per second

When a nuclide undergoes radioactive decay it breaks down to fall into a lower energy state expending the excess energy as radiation. The radioactivity released can be in the form of:

1. Alpha particles
2. Beta particles
3. Gamma particles (or photons)
4. Others

#### 1. Alpha particles

• Symbol: α
• Formed of 2 protons and 2 neutrons (i.e. a helium atom)
• Positively charged
• Relatively heavy
• Short range of travel

#### 2. Beta particles

• Symbol: β
• Electrons emitted from radioactive nuclei
• Carry negative charge
• Split into β- (negatron) and an antimatter equivalent β+ (positron)
• Lighter and smaller than α

#### 3. Gamma particles

• Symbol: γ
• Identical to x-rays except for the origin (x-rays originate from electron bombardment, gamma particles from radioactive atoms)
• Result of transition between nuclear energy levels
• Very high energy and range of travel

#### 4. Others

• X-rays
• Internal conversion: γ ray energy transferred to inner shell electron which is then emitted from the nucleus
• Auger electron: ejected from electron shells as a result of same radioactive decay processes that create electron shell vacancies. Competes with emission of x-rays.
• Neutrinos and anti-neutrinos: electrically neutral particles with very little mass emitted from atomic nuclei during β+ and β- decay respectively.
• Spontaneous fission: very heavy nuclides are so unstable they split into two smaller nuclides emitting neutrons in the process.

### Decay models

There are several ways in which a nuclide can decay to its more stable form. These are:

1. Alpha decay
2. β- decay
3. β+ decay (aka positron emission)
4. Electron capture
5. Isomeric transition
6. Gamma decay

#### 1. Alpha (α) decay

This occurs in heavier nuclides with too many nucleons. The parent nuclide emits a helium atom (α particle). This type of decay occurs in the nuclides in area C (yellow) of the decay model graph that are very heavy.

#### 2. Beta minus (β-) decay

This occurs in nuclides in area B (green) area of the decay model graph that have too many neutrons. The neutral neutron (n) decays into a positive proton (p) (which is retained in the nucleus), a negative electron (e) and an electron antineutrino (ve) (i.e. the charge on both sides of the equation remains the same). A neutron is lost and a proton is gained meaning the mass number (A, number of protons plus neutrons) remains equal but the atomic number (Z, number of protons) increases by 1.

np + e + ve

#### 3. Beta plus (β+) decay aka positron emission

This occurs in the nuclides in area A (red) of the decay model graph that have too few neutrons. The extra proton decays into a neutron (which is retained in the nucleus), a positron (β+ or e) and an electron neutrino (ve). A neutron is gained and a proton is lost meaning the mass number remains equal but the atomic number decreases by 1. This form of radioactivity, with the production of a positron, is important in PET imaging.

pn + β+/e + ve

#### 4. Electron capture

This competes with β+ decay as it also occurs in proton-rich nuclei. If the energy difference between the parent and daughter nuclides is too low for positron emission an inner shell electron is captured by the nucleus converting a proton into a neutron (i.e. positive + negative = neutral). As with β+ decay the mass number remains the same but the atomic number decreases by 1.

p + en

#### 5. Isomeric transition

A radionuclide in a metastable excited state decays to its ground state by isomeric transition and the number of protons and neutrons remain the same. The energy difference is emitted as γ radiation. The mass number and atomic number remain unchanged.

e.g. Tc-99m → Tc-99 + 140 keV γ rays

#### 6. Gamma (γ) decay

Gamma decay is released by a hyperexcited nucleus moving the nucleus to a lower energy state after β or α decay.

#### Points to help understanding

1. The charge on both sides of the equation must remain the same

2. Simplistically speaking, a neutron is made of a proton and an electron

n = p + e

n = +ve + -ve

• This means:
• A neutron will decay into a proton and an electron (β- decay)
• A proton and an electron will join to form a neutron (electron capture)

3. Simplistically speaking (again) a proton is made of a neutron and a positron (β+) (β+ decay)

p = n + β+

+ve = n + +ve

4. The mass (A) always remains the same except for in alpha decay

### Σ  Summary

• The number of protons in an atom determines its element
• Radionuclides transform into a more stable nuclide by releasing energy in the form of radiation
• Radioactivity is measured in Becquerels (Bq). 1 Bq = 1 transformation / second
• Radiation can be alpha, beta or gamma particles
• What is released and the method of decay depends on the characteristics of the radionuclide

 Type of decay Occurs in … Produces Daughter nuclide Alpha decay Heavy nuclei Helium atom (2p and 2n) A minus 4 Z minus 2 β- decay Too many neutrons n → p + e– + v–e neutron becomes proton and electron A equal Z plus 1 β+ decay Too few neutrons Too many protons p → n + β+ + ve proton becomes neutron and positron (β+) A equal Z minus 1 Electron capture Too few neutrons but not enough energy for β+ decay p + e– → n electron captured and combines with proton to form neutron A equal Z minus 1 Isomeric transition Metastable excited nuclides γ radiation A equal Z equal