Radioactivity is a natural process where unstable atomic nuclei spontaneously release energy and subatomic particles, transforming into more stable configurations. Alpha decay is a specific type of radioactive disintegration, involving the emission of a particular particle from an unstable nucleus.
The Basics of Alpha Decay
Alpha decay occurs primarily in very heavy, unstable atomic nuclei. These nuclei have an excess of both protons and neutrons, leading to an imbalance of forces. To achieve a more stable state, the nucleus ejects an alpha particle. This emitted alpha particle is identical to a helium-4 nucleus, consisting of two protons and two neutrons. The original unstable nucleus, called the parent nucleus, transforms into a new element, the daughter nucleus, after this emission.
Writing the Alpha Decay Equation
Alpha decay is represented by a nuclear equation showing the transformation of the parent nucleus into a daughter nucleus and an alpha particle. The general form is: $^A_Z X \rightarrow ^{A-4}_{Z-2} Y + ^4_2 He$. In this equation, ‘X’ is the parent nucleus, ‘Y’ is the daughter nucleus, and ‘$^4_2 He$’ symbolizes the alpha particle. The superscript ‘A’ denotes the mass number (total protons and neutrons), while the subscript ‘Z’ indicates the atomic number (number of protons).
During alpha decay, two conservation laws are upheld: conservation of mass number and conservation of atomic number. The sum of mass numbers on the left side of the equation must equal the sum on the right. Similarly, the sum of atomic numbers on the left must equal the sum on the right. When a parent nucleus ‘X’ with mass number ‘A’ and atomic number ‘Z’ undergoes alpha decay, the daughter nucleus ‘Y’ will have a mass number of A-4 and an atomic number of Z-2. This reduction reflects the two protons and two neutrons carried away by the alpha particle.
Determining Energy Released
Energy is released during alpha decay due to mass defect. The combined mass of the daughter nucleus and the emitted alpha particle is slightly less than the mass of the original parent nucleus. This mass difference, known as the mass defect, is converted into energy according to Einstein’s mass-energy equivalence principle, E=mc². Here, ‘E’ represents the energy released, ‘m’ is the mass defect, and ‘c’ is the speed of light.
To calculate the energy released, first determine the mass defect by subtracting the total mass of the products (daughter nucleus and alpha particle) from the mass of the parent nucleus. This mass difference is expressed in atomic mass units (amu). The calculated mass defect is then converted into energy, measured in mega-electron volts (MeV), using the conversion factor: 1 amu ≈ 931.5 MeV/c². This resulting energy, known as the Q-value of the decay, is primarily carried away as kinetic energy by the alpha particle and the recoiling daughter nucleus.
Practical Calculation Examples
Consider the alpha decay of Uranium-238 ($^{238}_{92}U$). To write the decay equation, Uranium-238 is the parent nucleus. The alpha particle ($^4_2 He$) is emitted, reducing the mass number by 4 and the atomic number by 2. This transformation results in a daughter nucleus with a mass number of 234 and an atomic number of 90. The element with atomic number 90 is Thorium (Th).
The complete decay equation for Uranium-238 is: $^{238}_{92}U \rightarrow ^{234}_{90}Th + ^4_2 He$. To determine the energy released, use the atomic masses: Uranium-238 (238.0507826 amu), Thorium-234 (234.0435955 amu), and the alpha particle (4.0026032 amu). The total mass of the products is 234.0435955 amu + 4.0026032 amu = 238.0461987 amu.
The mass defect (Δm) is calculated as the mass of the parent minus the mass of the products: Δm = 238.0507826 amu – 238.0461987 amu = 0.0045839 amu. Converting this mass defect into energy using the conversion factor (1 amu = 931.5 MeV/c²), the energy released (Q-value) is Q = 0.0045839 amu 931.5 MeV/amu ≈ 4.270 MeV. This calculation demonstrates how both the resulting element and the energy output from alpha decay are determined.