The half-life of the goo in minutes is 20 minutes.
Initailly the amount of radioactive goo is 288 grams
Time taken is 120 minutes
amount of radioactive goo left is 4.5 gram
Number of half lives =
[tex](\frac{1}{2})^{n} = \frac{a}{a'} \\\\\frac{1}{2^n} = \frac{4.5}{288}\\\\ \frac{1}{2^n} = \frac{1}{64}[/tex]
2ⁿ = 64
2ⁿ = 2⁶
n = 6
The number of half lives is 6
half life = total time / number of half lives
= 120 / 6
= 20 minutes
Therefore, if at the beginning of an experiment, a scientist has 288 grams of radioactive goo. after 120 minutes, her sample has decayed to 4.5 grams, then the half-life of the goo in minutes is 20 minutes.
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