Reflection on Radioactive Decay and Half-Life Calculation

How can we calculate the amount of a radioactive isotope remaining after a certain period of time?

Using the data provided, what is the formula for calculating the remaining amount?

Final answer:

The amount of a radioactive isotope remaining after some time is calculated using the half-life formula, with Radium-226's half-life of 1,620 years and the initial sample mass factored into the equation.

Reflection on radioactive decay and half-life calculation involves understanding the concept of half-life and how it affects the decay of radioactive isotopes. Radioactive decay occurs when unstable atoms undergo changes in their nucleus to become more stable. This process results in the emission of radiation and the transformation of the original element into a different element or isotope.

One key aspect of radioactive decay is the concept of half-life. Half-life is the time it takes for half of the radioactive atoms in a sample to decay. It is a characteristic property of each radioactive isotope and can be used to determine the rate of decay and the amount of the isotope remaining over time.

To calculate the remaining amount of a radioactive isotope after a certain period, we use the half-life formula. For Radium-226 with a half-life of 1,620 years, the decay formula is:

N = N0 × (1/2)^(t/t₁/₂)

where N is the final amount of the isotope, N0 is the initial amount, t is the time that has elapsed, and t₁/₂ is the half-life of the isotope. In the question with a 120-gram sample, we can plug these values into the formula to find the amount remaining after t years.