Understanding the Half-Life and the Rate of Radioactive Decay

Understanding the half-life and the rate of radioactive decay
The atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. Many elements have an unstable atomic nucleus, which leads to decay by emitting radioactivity, a phenomenon that has a very specific mathematical description. The decay rate and the half-life of the radioactive material are a measure of how quickly the nuclei will decay.

Radioactivity
During the process of radioactive decay, the unstable core emits particles or electromagnetic waves. The three main types of radioactivity are the decay of alpha, beta, and gamma. The alpha decay causes the emission of two protons and two neutrons from the atomic nucleus. Beta decay causes electron or positron emissions (anti-electron material) from the atomic nucleus. Finally, gamma decay causes electromagnetic gamma-ray emission.

Decay rate
Radioactivity has a very clear mathematical description that allows decay rates to be calculated. The number of radioactive nuclei, N, is given by mathematical expressions: N = N0e (-λt). In this equation, N0 represents the original number of cores, t represents time and λ is the decay rate. The rate of radioactive decay is negative, reflecting the decrease in the number of nuclei as time increases.

Halftime
Radioactive half-life is defined as the amount of time taken to reduce the core count by 50 percent. Mathematically, the half-life can be written in the decay rate: half-life = - ln (2) / λ. The natural logarithm (ln) is a mathematical function that is the opposite of the exponential function (e). You can find natural logarithms on a scientific calculator where it will be labeled "ln." Calculates decay rate and half life

The rate of radioactive decay can be calculated from the half-life. Rearrange the above equation to calculate the half-life so that the equation becomes as follows:

λ = - ln (2) / half-life,

decay rate can be calculated by dividing ln (2) by half-life. For example, Radium-226 has a half-life of 1,601 years. This means that it has a decay rate: λ = -ln (2) / 1601 = -0.00043