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.