Question

A certain radioactive material has half life of 200 years. Find the time required of a given amount to become one tenth of its original mass.

Answer 1

A Challenging question for anyone willing to solve it

Answer 2

\[A = A_{0} * (1/2)^{\frac{ t }{ t0} }\]
where A is the final amount, A0 is the initial amount, t is the time, t0 is the half-life (sorry if it's hard to see, but it's (1/2) ^ (t / t0)

in this case, you can let your original amount be x (it doesn't actually matter cause it'll cancel out). therefore, "to become 1/10 of its original mass" ---> (1/10)x is the final amount.

t0, the half-life, is also given as 200 years

so you have:\[(1/10)x =x * (1/2)^{\frac{ t }{ 200} }\]
x cancels out on both sides, so you can just solve for x. (would strongly recommend using a calculator)

Answer 3

*solve for t, not x, sorry

Answer 4

You are really smart