Band of Stability: Electron Capture and Positron Emission

Band of Stability: Electron Capture & Positron Emission

Understanding Nuclear Stability

The band of stability refers to the region on a neutron-to-proton (N/Z) plot where stable nuclei are found. Nuclei outside this band tend to undergo radioactive decay to achieve greater stability. Two important decay processes for nuclei with a low neutron-to-proton ratio are electron capture and positron emission.

• Electron Capture: A process in which an inner orbital electron is captured by the nucleus, combining with a proton to form a neutron. This decreases the atomic number by one while the mass number remains unchanged.

• Positron Emission: A process in which a proton in the nucleus is converted into a neutron with the emission of a positron (β+). This also decreases the atomic number by one, with no change in mass number.

Neutron-to-Proton (N/Z) Plot

The N/Z plot visually represents the stability of nuclei. The band of stability is the region where stable isotopes are found. Nuclei above or below this band are unstable and will undergo radioactive decay to move toward the band.

• Nuclei above the band (high N/Z): Tend to undergo beta decay (not shown here).

• Nuclei below the band (low N/Z): Tend to undergo electron capture or positron emission.

Electron Capture and Positron Emission: Equations

• Electron Capture:

  • General equation: $^A_ZX + ^0_{-1}e \rightarrow ^A_{Z-1}Y$

  • Where $^A_ZX$ is the parent nuclide, $^0_{-1}e$ is the captured electron, and $^A_{Z-1}Y$ is the daughter nuclide.

• Positron Emission:

  • General equation: $^A_ZX \rightarrow ^A_{Z-1}Y + ^0_{+1}e$

  • Where $^A_ZX$ is the parent nuclide, $^A_{Z-1}Y$ is the daughter nuclide, and $^0_{+1}e$ is the emitted positron.

Example: Electron Capture of Strontium-81

Question: Provide the identity of the daughter nuclide created from the electron capture of strontium-81.

• Solution: Strontium-81 ($^{81}_{38}Sr$) undergoes electron capture:

$^{81}_{38}Sr + ^0_{-1}e \rightarrow ^{81}_{37}Rb$

• The daughter nuclide is Rubidium-81 ($^{81}_{37}Rb$).

Practice: Positron Emission of Strontium-81

Question: Provide the identity of the daughter nuclide created from the positron emission of strontium-81.

• Solution: Strontium-81 ($^{81}_{38}Sr$) undergoes positron emission:

$^{81}_{38}Sr \rightarrow ^{81}_{37}Rb + ^0_{+1}e$

• The daughter nuclide is Rubidium-81 ($^{81}_{37}Rb$).

Summary Table: Electron Capture and Positron Emission

Process	Equation	Change in Atomic Number (Z)	Change in Mass Number (A)	Example (Sr-81)
Electron Capture	$^A_ZX + ^0_{-1}e \rightarrow ^A_{Z-1}Y$	-1	0	$^{81}_{38}Sr + ^0_{-1}e \rightarrow ^{81}_{37}Rb$
Positron Emission	$^A_ZX \rightarrow ^A_{Z-1}Y + ^0_{+1}e$	-1	0	$^{81}_{38}Sr \rightarrow ^{81}_{37}Rb + ^0_{+1}e$

Additional info: Both processes are common for nuclides with a low neutron-to-proton ratio (below the band of stability), helping them achieve a more stable configuration by increasing the relative number of neutrons.