The half-life of Thorium - 232 is 14 billion years. If you started with 26 grams of Thorium, how many grams would you have left after 7 half-lives?
A) 0.203
B) 0.101
C) 0.05

A) 0.203 g

Explanation:

A radioactive isotope is an isotope that decays over time. The equation that describes the radioactive decay or an isotope is

where

is the initial mass of the isotope at time t = 0

is the mass of the isotope after time t

t is the time

is the half-life of the isotope, which is the time taken for the amount of isotope to halve

In this problem, we have:

is the initial mass of the sample of Thorium-232

is the half-life of the sample

Here we want to find the amount of thorium left after 7 half-lives, so when

Substituting into the equation, we find:

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