The decay constant of plutonium-239, a waste product from nuclear reactors, is 2.88 * 10-5 year - 1. What is the half-life of 239Pu?

Verified step by step guidance

1. Identify the decay constant (λ) given in the problem. For plutonium-239, λ is 2.88 * 10^-5 year^-1.
2. Recall the relationship between the decay constant (λ) and the half-life (T_1/2) of a radioactive isotope, which is given by the formula: T_1/2 = ln(2) / λ.
3. Substitute the value of λ into the formula. Use the natural logarithm of 2 (ln(2)) which is approximately 0.693.
4. Perform the division to solve for T_1/2.
5. Express the half-life in appropriate units, which in this case would be years, to match the units of the decay constant.

Key Concepts

Decay Constant

The decay constant (λ) is a probability rate at which a radioactive isotope decays. It is specific to each isotope and is expressed in units of time inverse, such as year⁻¹. A higher decay constant indicates a faster rate of decay, while a lower value suggests a slower decay process.

Half-Life

Half-life is the time required for half of the radioactive nuclei in a sample to decay. It is a crucial concept in nuclear chemistry, as it provides insight into the stability and longevity of radioactive materials. The half-life can be calculated using the decay constant with the formula t₁/₂ = ln(2)/λ.

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This process can result in the transformation of one element into another and occurs at a predictable rate characterized by the decay constant. Understanding this process is essential for calculating the remaining quantity of a radioactive substance over time.