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The activity of a radioactive sample is decreased by 75% of the initial value after 60 days. The half life (in days) of the sample is approximately is ____.
Correct answer is '30'. Can you explain this answer?
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The half-life of a radioactive sample is the time it takes for half of the radioactive atoms in the sample to decay. In this case, we are given that the activity of the sample is decreased by 75% after 60 days.
Let's assume the initial activity of the sample is A0. After 60 days, the activity of the sample is decreased by 75%, which means it is now at 25% of its initial value. Mathematically, this can be expressed as:
A60 = 0.25 * A0
We can also express this in terms of the remaining fraction of the sample:
R60 = A60/A0 = 0.25
Now, we can use the concept of half-life to find the half-life of the sample. The half-life is the time it takes for the remaining fraction of the sample to reduce to half its initial value. In this case, the remaining fraction after 60 days is 0.25.
Let's assume the half-life is T. After T days, the remaining fraction of the sample will be 0.5:
R(T) = 0.5
We can now set up the following equation:
0.5 = A(T)/A0
Since we know that A(T) = 0.25 * A0, we can substitute this into the equation:
0.5 = 0.25 * A0 / A0
Simplifying the equation, we get:
0.5 = 0.25
Since this equation is true, it means that the half-life of the sample is equal to 60 days.
Let's assume the initial activity of the sample is A0. After 60 days, the activity of the sample is decreased by 75%, which means it is now at 25% of its initial value. Mathematically, this can be expressed as:
A60 = 0.25 * A0
We can also express this in terms of the remaining fraction of the sample:
R60 = A60/A0 = 0.25
Now, we can use the concept of half-life to find the half-life of the sample. The half-life is the time it takes for the remaining fraction of the sample to reduce to half its initial value. In this case, the remaining fraction after 60 days is 0.25.
Let's assume the half-life is T. After T days, the remaining fraction of the sample will be 0.5:
R(T) = 0.5
We can now set up the following equation:
0.5 = A(T)/A0
Since we know that A(T) = 0.25 * A0, we can substitute this into the equation:
0.5 = 0.25 * A0 / A0
Simplifying the equation, we get:
0.5 = 0.25
Since this equation is true, it means that the half-life of the sample is equal to 60 days.
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The activity of a radioactive sample is decreased by 75% of the initial value after 60 days. The half life (in days) of the sample is approximately is ____.Correct answer is '30'. Can you explain this answer?
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