Question

The half-life of a radioactive kind of cerium is 32 days. If you start with 84,288 grams of it, how much will be left after 160 days?

Answer 1

ANSWER

$2,634g$

EXPLANATION

To find the amount left after 160 days, we have to apply the formula for the amount of a substance remaining using its half-life:

$N=N_0(\frac{1}{2})^{\frac{t}{T_{}}}$

where N0 = initial amount of the substance

t = time elapsed

T = half-life

Therefore, we have that the amount of Cerium left after 160 days is:

$\begin{gathered} N=84,288\cdot(\frac{1}{2})^{\frac{160}{32}} \\ N=84,288\cdot(\frac{1}{2})^5=84,288\cdot0.03125 \\ N=2,634g \end{gathered}$

Hence, 2,634 grams of Cerium will be left.