24. α-, and β-decay. γ-radiation.

Question 1

Explain the reason for unstable nuclei

Answer 1

If the nucleus is unstable, it has the tendency of emitting some kind of radiation (= radioactivity).

The stability/instability of atoms can be determined in 3 steps:

1) Odds-even concept (→ table)

2) Magic numbers:

But there are so called magic numbers which are natural occurrences in isotopes and are stable. Isotopes that have these numbers occurring in either the proton or neutron are stable.

• proton: 2, 8, 20, 28, 50, 82, 114
• neutron: 2, 8, 20, 28, 50, 82, 126, 184

3) N/Z ratio:

Usually the stability of an atom depends on its NZ ratio, the stronger the repulsion force, the more neutrons are needed to stabilize the nuclei.

• ​for Z < 20 = N/Z 1:1
• for Z 20-83 = N/Z 1.5:1
• for Z > 83 = radioactive

Question 2

List different kinds of radioactive decay according to the diagram below and name it

Answer 2

Types of radioactive decay:

• α-decay → α-particle = ⁴₂He nucleus
• β-decay → β⁺ = positron, β^- = electron
• γ-radiation → γ-ray
• K-electron capture → X-ray photon

Band (belt) of stability:

• higher end: alpha decay,
• below: positron emission or electron capture
• above: beta emissions

Question 3

Explain the band (belt) of stability

Answer 3

Graph of isotopes by type of nuclear decay. Orange and blue nuclides are unstable, with the black squares between these regions representing stable nuclides. The unbroken line passing below many of the nuclides represents the theoretical position on the graph of nuclides for which proton number is the same as neutron number. The graph shows that elements with more than 20 protons must have more neutrons than protons, in order to be stable.

Question 4

Describe the features of α-decay and relate it to its position on the belt of stabilty

Answer 4

Features:

• typical for heavy atoms
• an α-particle (⁴₂He-nucleus) will be emitted ^A_ZX → ^A-4_Z-2Y + ⁴₂α
• line E-spectrum (E_kin of atom + α-particle = nuclear recoil)
• E_α in MeV range

Alpha decay is located at the top of the plotted line, because the alpha decay decreases the mass number of the element in order to keep the isotope stable.

Because the isotope was originally unstable before it went through alpha decay, the elements are still considered unstable.

Question 5

Describe the features of β-decay and relate it to its position on the belt of stabilty

Answer 5

We distinguish between:

β^--decay:

• happens in case of neutron surplus
• a β^--particle (= e^-) and antineutrino are emitted ¹₀n → ¹₁p + ⁰_-1β + v[Bar]

β⁺-decay:

• happens in case of proton surplus
• a β⁺-particle (= positron) and neutrino are emitted ¹₁p → ¹₀n + ⁰₊₁β + v

Similarities:

continuous E-spectrum (for both) (either a v or v[Bar] is emitted as well, there is a spectrum of E for the electron or positron, depending upon what fraction of the reaction energy Q is carried by the massive particle)

β⁺-decay accepts protons so it changes the amount of protons and neutrons, the no. of protons increase while neutrons decrease. To make things easier to understand think of the ratio of the isotope: there are too many neutrons compared to the no. of protons therefore it is above the band of stability.

Question 6

Describe the features of γ-decay

Answer 6

We distinguish between:

Prompt γ-radiation:

• surplus E emitted immediately in form of γ-radiation

​

​Isomeric transition:

If excited state of daughter nucleus metastable → γ-radiation emitted later

Similarities:

• energetically unfavoured arrangement of nucleons in the daughter nucleus (after α-/β-decay)
• BUT: mass number unchanged

Question 7

Define metastability

Answer 7

Metastability denotes the phenomenon when an isolated system spends an extended time in a configuration other than the system’s state of least E.

Question 8

Describe the features of **k-capture **(= electron capture, inverse β-decay)

Answer 8

K-capture is a process in which a proton-rich nuclide absorbs an inner atomic electron, thereby changing a nuclear proton to a neutron and simultaneously causing the emission of an electron neutrino.

• 11p+ 0-1β→ 10n+ν
• atomic mass unchanged, but new element
• new element in excited state
• outer shell e- fills missing inner shell e- (→ ground state)
• X-ray photon emitted