Determining half-life of a radioactive sample

[doubledouble]

If I know that a sample of X has a half-life of 270 years how do I confirm this experimentally? What data would I have to collect? How about if the half-life of X was much shorter i.e. in terms of days?

 

[Zorodius]

Use some kind of device capable of measuring radiation quantitatively, like a geiger counter. With this, you can discover how much the sample is radiating at some point in time.

Where k, c, and A are unknown constants, x is the amount of radioactive matter remaining, L is the half-life, and t is time, you can reason out what measurements you'd need this way:

radiation (change in amount of radioactive material in the sample) = k multiplied by amount remaining
dx / dt = k x
dx / x = k dt
ln x = k t + c (integrate both sides)
x = A e^kt (exponentiate both sides, let A = e^c)

for the half-life:

0.5 A = A e^kL (half of the amount at t=0 will remain at t=L)
(ln 0.5)/L = k

so from knowing L, you know k.

measure dx / dt, divide by k, and you know a value for x.

Repeat the same experiment at other times, recording x and t for each.

If the values you measure satisfy x = A e^kt for the value of k you calculated, then you are right about L.

If they do not work, you can use the equation to find the true value of k and L.

 

[sir-pinski]

To confirm the half-life of a radioactive sample experimentally, you would need to collect data on the decay of the sample over a period of time. This can be done by measuring the amount of radioactive material remaining at different time intervals.

If the half-life of X is 270 years, you would need to measure the amount of X remaining after 270 years, 540 years, 810 years, and so on. By plotting this data on a graph, you should see a pattern of exponential decay, where the amount of X decreases by half every 270 years.

To further confirm this, you can also measure the amount of X remaining at shorter time intervals, such as after 135 years, 67.5 years, and so on. The results should still follow the same pattern of exponential decay, with the amount of X decreasing by half every 270 years.

If the half-life of X is much shorter, such as in terms of days, the same method can be applied. You would need to measure the amount of X remaining after a certain number of days, and then plot the data on a graph. The pattern should still show exponential decay, with the amount of X decreasing by half every half-life interval.

In addition to measuring the amount of X remaining, you can also collect data on the decay rate of X. This can be done by measuring the amount of radiation emitted by the sample at different time intervals. The decay rate should also follow the same pattern of exponential decay, with the rate decreasing by half every half-life interval.

Overall, by collecting data on the amount of X remaining and the decay rate, you can confirm the half-life of a radioactive sample experimentally. The key is to measure the sample at different time intervals and observe the pattern of exponential decay.