Explanation:
The half-life of a radioactive substance is the time it takes for half of the initial amount to decay. It is denoted by t1/2.

Formula:
The formula for calculating the half-life of a radioactive substance is given by:

Nt = N0 (1/2)^(t/t1/2)

Where,
Nt = final amount of the substance
N0 = initial amount of the substance
t = time
t1/2 = half-life of the substance

Solution:
Given, initial amount of radioactive isotope, N0 = 10 grams
Final amount of radioactive isotope, Nt = 1.25 grams
Time, t = 12 years

Using the formula, we get:

1.25 = 10 (1/2)^(12/t1/2)
0.125 = (1/2)^(12/t1/2)
log(0.125) = log[(1/2)^(12/t1/2)]
log(0.125) = (12/t1/2)log(1/2)
log(0.125) = (-0.693/t1/2) * 12
t1/2 = (-0.693 * 12) / log(0.125)
t1/2 = 18.42 years (approx)

Therefore, the half-life period of the radioactive isotope is 18.42 years.

Conclusion:
The half-life of a radioactive substance is an important parameter in determining its stability and rate of decay. The longer the half-life, the more stable the substance is. In this case, the half-life of the radioactive isotope is 18.42 years, which means that it takes 18.42 years for half of the initial amount of the substance to decay.