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
Nathan L.
May 27, 2017

#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"#

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