How many half-lives does it take a radioactive substance to decay until only one-eighth of the original substance remains?
a
three
b
eight
c
six
d
two
c) six
To find the answer, we need to understand the concept of radioactive decay and how it relates to the number of half-lives.
Radioactive substances decay over time, and their decay can be measured in terms of half-lives. The half-life is the amount of time it takes for half of the substance to decay. After each half-life, half of the remaining substance decays, leaving only half of what was there before.
In this case, we want to know how many half-lives it takes for a radioactive substance to decay until only one-eighth (1/8) of the original substance remains.
Starting with the initial substance, we go through the following steps:
1. After the first half-life, half of the substance decays, leaving only 1/2 of the original substance.
2. After the second half-life, half of the remaining substance decays, leaving only 1/4 of the original substance.
3. After the third half-life, half of the remaining substance decays, leaving only 1/8 of the original substance.
From these steps, we can see that it takes three half-lives for a radioactive substance to decay until only one-eighth of the original substance remains.
Therefore, the correct answer is option a) three.
To determine the number of half-lives it takes for a radioactive substance to decay until only one-eighth of the original substance remains, we can use the formula:
Remaining amount = (1/2)^(number of half-lives)
Given that we want to find when one-eighth, or (1/8), of the original substance remains, we can set up the equation as follows:
(1/8) = (1/2)^(number of half-lives)
To solve for the number of half-lives, we can take the logarithm of both sides of the equation:
log(1/8) = log[(1/2)^(number of half-lives)]
Using the logarithmic property log(base a)(x^y) = y * log(base a)(x), we can rewrite the equation as:
log(1/8) = (number of half-lives) * log(1/2)
Since log(1/8) can be expressed as -3, and log(1/2) can be expressed as -1, we can substitute these values into the equation:
-3 = (number of half-lives) * (-1)
Now, we can solve for the number of half-lives:
-3 = -1 * (number of half-lives)
number of half-lives = 3
Therefore, it would take three half-lives for a radioactive substance to decay until only one-eighth of the original substance remains.
The correct answer is a) three.