Question 1204528
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If 250 mg of a radioactive element decays to 190 mg in 36hrs find the half-life of the element.
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<pre>
The formula for the decay mass in terms of half-life is

    M(t) = {{{M[0]*(1/2)^(t/T)}}},    (1)

where t i the time; T is the half-life time, M(t) is the current remaining mass; {{{M[0]}}} is initial mass.


We are given  {{{M[0]}}} = 250 mg;  t = 36 hours.;  M(t) = 190 mg;    We need to fint half-life T.


The basic equation (1) takes the form

    190 = {{{250*(1/2)^(36/T)}}}.


Divide both sides by 250.  You will get

    {{{190/250}}} = {{{(1/2)^(36/T)}}}

or

    0.76 = {{{(1/2)^(36/T)}}}.


Take logarithm base 10 of both sides

    log(0.76) = {{{-(36/T)*log((2))}}}.


Express T

    T = {{{-36*(log(2))/log((0.76)))}}} = calculate and get = 90.9255 hours = 90 hours and 53 minutes (approximately).


<U>ANSWER</U>.  Half-life is about 90 hours and 53 minutes.
</pre>

Solved.


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