After 10 years, 75 g of an original sample of 100 g of a certain radioactive isotope has decayed. the half-life of the isotope is

Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value. The formula that describe the exponential decay is:
N(t)=N0 (1/2)∧(t/t(1/2))
where
N0 is the initial quantity
Nt is the remaining quantity after time, t
t(1/2) is the half-life

So, t(1/2) = (-㏑2)*t/㏑(Nt/N0) = (-㏑2)*10/㏑((100-75)/100) = 5 years.
The half-life of this isotope is 5 years.

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