Question

You have 7,232 grams of a radioactive kind of uranium. How much will be left after 56 hours if its half-life is 14 hours?

Answer 1

`452 "g U"`

Explanation:

We're asked to find how much uranium remains after a given time (`56 "hr"`), when given its initial amount (`7232 "g"`) and its half-life (`14 "hr"`).

When solving half-life problems like this one, we can use the equation

`m(t) = m_0(1/2)^((t)/(t_(1/2)`

where
`m(t)` is the mass of the remaining mass of the decaying substance,
`m_0` is the initial mass of the substance,
`t` is the time (in whatever the unit the half-life is, in this case hours), and
`t_(1/2)` is the half-life of the substance.

(In case it's difficult to see, the exponent on the `1/2` is `t/(t_(1/2))`)

Plugging in known variables, the equation becomes

`m(t) = (7232"g")(1/2)^((56cancel("hr"))/(14 cancel("hr"))`

`= color(red)(452 "g U"`