Band of Stability, Alpha Decay, and Nuclear Fission

Band of Stability, Alpha Decay, and Nuclear Fission

Band of 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 are unstable and tend to undergo radioactive decay to move toward stability.

• Stable nuclei have a balanced ratio of neutrons (N) to protons (Z).

• Nuclei above the band (high N/Z) are neutron-rich and tend to undergo beta decay.

• Nuclei below the band (low N/Z) are proton-rich and tend to undergo positron emission or electron capture.

• Very heavy nuclei (high Z) are often unstable due to excessive repulsive forces between protons and may undergo alpha decay or nuclear fission.

Alpha Decay

Alpha decay is a type of radioactive decay in which an unstable nucleus emits an alpha particle (consisting of 2 protons and 2 neutrons, equivalent to a helium-4 nucleus). This process decreases both the atomic number and mass number of the parent nucleus.

• Alpha particle: $^4_2\text{He}$ or $\alpha$

• General equation:

$^A_Z\text{X} \rightarrow ^{A-4}_{Z-2}\text{Y} + ^4_2\text{He}$

• Alpha decay is common in heavy nuclei (Z > 82) to reduce both mass and proton number, moving the nucleus toward the band of stability.

Example: The alpha decay of uranium-238:

$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^4_2\text{He}$

Neutron-to-Proton Plot

The neutron-to-proton (N/Z) plot visually represents the band of stability. Stable nuclei cluster along a curve where N/Z is optimal for stability. Alpha decay moves nuclei toward this band by reducing both N and Z.

Nuclear Fission

Nuclear fission is a nuclear reaction in which a heavy nucleus splits into two (or more) lighter nuclei, along with the release of a large amount of energy and several free neutrons. This process is the basis for nuclear reactors and atomic bombs.

• Fission is typically induced by neutron absorption in heavy nuclei (e.g., uranium-235).

• The products are two (or more) smaller nuclei (fission fragments), free neutrons, and energy.

• The released neutrons can induce further fission reactions (chain reaction).

General equation:

$^{235}_{92}\text{U} + ^1_0\text{n} \rightarrow ^{141}_{56}\text{Ba} + ^{92}_{36}\text{Kr} + 3^1_0\text{n}$

• Actual fission products vary, but the sum of mass and atomic numbers is conserved.

Example: Fission of uranium-235 produces krypton-92 and barium-141, along with three neutrons:

$^{235}_{92}\text{U} + ^1_0\text{n} \rightarrow ^{92}_{36}\text{Kr} + ^{141}_{56}\text{Ba} + 3^1_0\text{n}$

Neutron-to-Proton Plot in Fission

Fission fragments are often neutron-rich and may undergo further beta decay to reach the band of stability.

Table: Comparison of Alpha Decay and Nuclear Fission

Process	Parent Nucleus	Products	Change in Mass Number (A)	Change in Atomic Number (Z)
Alpha Decay	Heavy nucleus (Z > 82)	Daughter nucleus + $^4_2\text{He}$	-4	-2
Nuclear Fission	Very heavy nucleus (e.g., $^{235}\text{U}$)	2 lighter nuclei + neutrons	Varies (split into two major fragments)	Varies (split into two major fragments)

Practice Example

• Alpha Decay Example: Which daughter nucleus would reside in the band of stability created from the alpha decay of lead-212?

• Solution: $^{212}_{82}\text{Pb} \rightarrow ^{208}_{80}\text{Hg} + ^4_2\text{He}$

• So, the daughter nucleus is mercury-208.

• Nuclear Fission Example: Nuclear fission of uranium-235 produces krypton-92 and barium-141, along with three neutrons.

• Missing daughter nucleus in a fission reaction can be determined by balancing mass and atomic numbers.

Key Terms

• Alpha particle ($\alpha$): Helium-4 nucleus ($^4_2\text{He}$)

• Band of stability: Region on N/Z plot where stable nuclei are found

• Nuclear fission: Splitting of a heavy nucleus into lighter nuclei with energy release

• Neutron-to-proton ratio (N/Z): Determines nuclear stability