# The radioactive element thorium-234 has a half-life of approximately 24 days. If I started with 82 grams of it, how much thorium would remain after 96 days?

Jun 5, 2018

$\text{5.125 g}$

#### Explanation:

If $96$ days is $\text{n}$ half lives then

$\text{n" = "96 days"/("24 days/half life") = "4 half lives}$

Amount of radioactive substance left after $\text{n}$ half lives is given by

"N"_t = "N"_0/(2^"n")

Where

• ${\text{N}}_{0} =$Initial Amount
• ${\text{N}}_{t} =$Amount left after $\text{n}$ half lives
• $\text{n =}$ Number of half lives

$\frac{\text{N"_t = "82 g}}{2} ^ 4$

color(white)("N"_t) = "82 g"/16

color(white)("N"_t) = "5.125 g"