The activity of aradioactive source falls to one sixteenth of originally value in 32 minutes. What is the hali- life
The half-life of the radioactive source is 8 minutes.
Explanation:
Half-life is the time taken for the activity (or amount) of a radioactive substance to reduce to half of its original value.
Given that the activity falls to one-sixteenth of its original value, it means the activity has reduced to 1/2^4 or 1/16th of its initial value after one-half life. (Each half-life reduces the activity to half of the previous value, so four half-lives will reduce it to 1/16th of the original value.)
We are told that this happens in 32 minutes, which is equivalent to four half-lives. Therefore, the time taken for one half-life is 32/4 = 8 minutes.
To find the half-life of a radioactive source, we can use the following formula:
t1/2 = t / log2(N0/Nt)
Where:
t1/2 = half-life
t = time elapsed
N0 = initial activity
Nt = final activity
Given that the activity of the radioactive source falls to one-sixteenth (1/16) of its original value in 32 minutes, we can conclude that the final activity is Nt = (1/16) * N0.
Now, we can plug in the values into the formula and solve for the half-life:
t1/2 = 32 / log2(N0/((1/16) * N0))
Simplifying further:
t1/2 = 32 / log2(16)
t1/2 = 32 / 4
t1/2 = 8
Therefore, the half-life of the radioactive source is 8 minutes.