The half-life of a radioactive material is about 34.6 years. How much of a 1-gram sample of the material is left after 30 years?
amount = 1 (1/2)^(30/34.6)
= .5^.8670...
= .548266 gram
To find the remaining amount of a substance after a given time, we can use the half-life formula. The half-life formula is:
N(t) = N₀ * (1/2)^(t / T)
Where:
N(t) is the remaining amount of the substance after time t
N₀ is the initial amount of the substance
t is the given time
T is the half-life of the substance
In this case, the initial amount (N₀) is 1 gram, the given time (t) is 30 years, and the half-life (T) is 34.6 years.
Substituting these values into the formula, we get:
N(30) = 1 * (1/2)^(30 / 34.6)
To calculate this using a calculator or a programming language, we can evaluate (1/2)^(30 / 34.6). The result will give us the remaining amount of the substance after 30 years.