Understanding Radioactive Decay: Calculating Isotope Amount Left
What is the formula to calculate the amount of an isotope left after a certain period of time?
A(t) = 217 € -0.0171
How can we find the amount left after 20 years?
The amount left after 20 years = 154.15 mg
Explanation:
Radioactive decay is a natural process where unstable atomic nuclei lose energy by emitting radiation. The amount of an isotope can be calculated using the decay formula A(t) = 217 € -0.0171t, where t is the time in years since the initial amount of 217 mg was present.
After substituting t with 20 years into the formula, we get:
A(t) = 217 € -0.0171 x 20
A(t) = 217 € -0.342
A(t) = 154.15 mg
Radioactive decay occurs due to the instability of atomic nuclei. Radioactive elements emit alpha (α), beta (β), and gamma (γ) particles during the decaying process.
The decay formula for an isotope is A(t) = 217 e^(-0.0171t), where A(t) represents the amount of the isotope at time t. In this case, we calculated the amount left after 20 years by substituting t with 20 in the formula and solving for A(t).
It is important to understand the concept of radioactive decay and how to calculate the remaining amount of an isotope after a specific period of time for various scientific and practical applications.