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Answer :
If the half-life of a radioactive isotope is 10 minutes then it will take 30 minutes for an 80 g sample to decay to 10 grams.
What is half-life?
The phrase is frequently used in nuclear physics to refer to how long stable atoms last or how quickly unstable atoms decay radioactively. In a broader sense, the phrase is used to describe any kind of exponential decay.
The half-life of an element is given by the formula
N(t) = N(0) × [tex]0.5^{\frac{t}{T}}[/tex]
N(t) = remaining quantity of a substance after time t
N(0) = initial quantity of the substance
T = half-life
Given:
Half-life, T = 10 minutes
N(t) = 10 g
N(0) = 80g
So, according to the half-life formula
10 = 80 × [tex]0.5^{\frac{t}{10}}[/tex]
[tex]0.5^{\frac{t}{10}}[/tex] = 1/8
t = [tex]\frac{10ln(\frac{1}{8})}{ln(0.5)}[/tex]
t = 30 minutes
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