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

`2,634g`

Step-by-step 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((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((1)/(2))^{(160)/(32)} \\ N=84,288\cdot((1)/(2))^5=84,288\cdot0.03125 \\ N=2,634g \end{gathered}`

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