How many half-lives does it take a radioactive substance to decay until only one-eighth of the original substance remains? a three b two c six d eight
The number of half-lives it takes for a radioactive substance to decay can be calculated using the formula N = (1/2)^n, where N is the fraction remaining and n is the number of half-lives.
In this case, we want to find the number of half-lives it takes until only one-eighth (1/8) of the original substance remains.
Using the formula:
(1/2)^n = 1/8
2^-3 = 2^(1/n)
-3 = 1/n
To solve for n, we can multiply both sides of the equation by -1:
3 = -1/n
Therefore, n = -1/3.
Since the number of half-lives cannot be negative, we round up to the nearest whole number.
Thus, it takes three half-lives for a radioactive substance to decay until only one-eighth of the original substance remains.
The correct answer is a) three.