The half-life of this americium nuclide is 470 years. A sample of this nuclide contains 8.0x10^14 atoms. After some time, 6 * 10 ^ 14 americium atoms have decayed.Calculate the time required for this decay
Question
The half-life of this americium nuclide is 470 years. A sample of this nuclide contains 8.0x10^14 atoms. After some time, 6 * 10 ^ 14 americium atoms have decayed.Calculate the time required for this decay
Solution
To solve this problem, we need to use the formula for radioactive decay, which is:
N = N0 * (1/2)^(t/T)
where: N is the final quantity of the substance N0 is the initial quantity of the substance t is the time that has passed T is the half-life of the substance
In this case, we know that: N0 = 8.0x10^14 atoms N = N0 - 6.0x10^14 atoms = 2.0x10^14 atoms T = 470 years
We need to solve for t. Plugging in the known values, we get:
2.0x10^14 = 8.0x10^14 * (1/2)^(t/470)
Solving for t, we get:
(1/2)^(t/470) = 2.0x10^14 / 8.0x10^14 (1/2)^(t/470) = 0.25 t/470 = log2(0.25) t = 470 * log2(0.25)
Using a calculator, we find that log2(0.25) is approximately -2. So:
t = 470 * -2 = -940 years
However, time cannot be negative. This means that our initial assumption that the nuclide has not yet reached its half-life is incorrect. In fact, it has passed its half-life twice. Therefore, the correct time is:
t = 940 years
Similar Questions
Suppose the amount of a certain radioactive substance in a sample decays from 1.30mg to 800.μg over a period of 7.57 seconds. Calculate the half life of the substance.Round your answer to 2 significant digits.
The half life for the radioactive decay of rubidium-87 to strontium-87 is ×4.881010 years.Suppose nuclear chemical analysis shows that there is 0.337mmol of strontium-87 for every 1.000mmol of rubidium-87 in a certain sample of rock. Calculate the age of the rock.Round your answer to 2 significant digits.
Derive an expression that relates the half-life and the decay constant for a sample of aparticular radioactive nucleus. Calculate the half-life and decay constant for a radioactiveisotope sample if the initial number of radioactive atoms is 450 and this reduces to 63 after24.3 hours.
The half life for the radioactive decay of carbon-14 to nitrogen-14 is ×5.73103 years.Suppose nuclear chemical analysis shows that there is 0.414mmol of nitrogen-14 for every 1.000mmol of carbon-14 in a certain sample of rock. Calculate the age of the rock.Round your answer to 2 significant digits.
Uranium-235 has a half-life of 7.038×108 years.(i) Determine the time required for the mass of 235U in a sample originally containing 1.000 g of 235U to decrease to 0.125 g.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.