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?

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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?

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Answer 1 · 2017-05-27T02:59:46

$452 g U$ $452 "g U"$

Explanation:

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

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

$m (t) = m_{0} {(\frac{1}{2})}^{\frac{t}{t_{\frac{1}{2}}}}$ $m(t) = m_0(1/2)^((t)/(t_(1/2)$

where
$m (t)$ $m(t)$ is the mass of the remaining mass of the decaying substance,
$m_{0}$ $m_0$ is the initial mass of the substance,
$t$ $t$ is the time (in whatever the unit the half-life is, in this case hours), and
$t_{\frac{1}{2}}$ $t_(1/2)$ is the half-life of the substance.

(In case it's difficult to see, the exponent on the $\frac{1}{2}$ $1/2$ is $\frac{t}{t_{\frac{1}{2}}}$ $t/(t_(1/2))$ )

Plugging in known variables, the equation becomes

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

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

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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?

1 Answer

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