Please tell me the formula for these types of questions

The half life of the radio - active isotope is 8 hours

Explanation:

We can tell that half - life of this radio - active isotope will be the time span with which 100 cpm of the substance remains, as half of 100 cpm is 200 cpm. When 25 cm remains it takes the duration of 24 hours / 1 day.

25 cm / 200 cm = 1 / 8

Therefore 1 / 8 of the substance remains after 24 hours. We want to calculate the time it takes for 1 / 2 of the substance to remains, which should clearly be less than 24 hours,

1 / 2 1 / 2

24 / 3 = 8 hours - three half lives fit into 1 / 8, and hence 24 / 3 = 8 hours. We can check this solution by considering this 8 hours. After 8 hours one - half of the substance remains, or 100 cpm. After another 8 hours one - half of 100 cpm remains, or 50 cpm. And after another 8 hours one - half of 50 cpm remains, or 25 cpm. 3, 8 hours is a duration of 24 hours - the remaining amount being 25 cpm.