A radioactive sample contains 2.35 g of an isotope with a halflife of 3.8 days. What mass of the isotope remains after 7.0 days?

Verified step by step guidance

1. Identify the initial mass of the isotope, which is given as 2.35 g.
2. Determine the half-life of the isotope, which is 3.8 days.
3. Calculate the number of half-lives that have passed in 7.0 days by dividing 7.0 days by the half-life (3.8 days).
4. Use the formula for exponential decay: \( m = m_0 \times (\frac{1}{2})^{n} \), where \( m_0 \) is the initial mass, \( n \) is the number of half-lives, and \( m \) is the remaining mass.
5. Substitute the values into the formula to find the remaining mass of the isotope after 7.0 days.

Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This decay occurs at a predictable rate characterized by the half-life, which is the time required for half of the radioactive sample to decay into a more stable form.

Half-Life

Half-life is a specific time period during which half of a given quantity of a radioactive substance will decay. For example, if a substance has a half-life of 3.8 days, after this time, only half of the original amount will remain, allowing for calculations of remaining mass over multiple half-lives.

Exponential Decay Formula

The exponential decay formula is used to calculate the remaining quantity of a radioactive substance after a certain time. It is expressed as N(t) = N0 * (1/2)^(t/T), where N(t) is the remaining quantity, N0 is the initial quantity, t is the elapsed time, and T is the half-life. This formula allows for precise calculations of remaining mass based on time and half-life.