A rate of decay of a radioactive element is independent of temperature, pressure, Infact for any external conditions. A simple law discovered by Rutherford states that a certain fraction of any sample of radioactive element undergoes change in a unit time. If we start with 10 mg of the radioactive substance (t12 = 1day) , only 5mg will be left at the end of the first day. At the end of 2nd day 2.5 mg will be left and so on. λ = 2.303tlogaa − x A human body required the 0.01μ activity of radioactive substance after 24 hours. Half life of radioactive is 6 hours. Then injection of maximum activity of radioactive substance that can be injected:
Question
A rate of decay of a radioactive element is independent of temperature, pressure, Infact for any external conditions. A simple law discovered by Rutherford states that a certain fraction of any sample of radioactive element undergoes change in a unit time. If we start with 10 mg of the radioactive substance (t12 = 1day) , only 5mg will be left at the end of the first day. At the end of 2nd day 2.5 mg will be left and so on. λ = 2.303tlogaa − x A human body required the 0.01μ activity of radioactive substance after 24 hours. Half life of radioactive is 6 hours. Then injection of maximum activity of radioactive substance that can be injected:
Solution
The question is asking for the maximum activity of a radioactive substance that can be injected into a human body, given that the body requires 0.01μ activity after 24 hours and the half-life of the radioactive substance is 6 hours.
First, we need to understand the concept of half-life. Half-life is the time required for a quantity to reduce to half its initial value. In this case, the half-life of the radioactive substance is 6 hours, which means that every 6 hours, the activity of the substance reduces to half its initial value.
Given that the body requires 0.01μ activity after 24 hours, we can calculate the initial activity that would have reduced to this value after 24 hours. Since the half-life is 6 hours, there are 4 half-lives in 24 hours.
Let's denote the initial activity as A. After one half-life (6 hours), the activity would be A/2. After two half-lives (12 hours), the activity would be A/4. After three half-lives (18 hours), the activity would be A/8. And after four half-lives (24 hours), the activity would be A/16.
So, if the activity after 24 hours is 0.01μ, we can set up the equation:
A/16 = 0.01μ
Solving for A, we get:
A = 0.01μ * 16 = 0.16μ
So, the maximum activity of the radioactive substance that can be injected into the human body is 0.16μ.
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