Calculating Delivery Time for Nuclides A & B

[shamone]

In a reactor and sepertation plant complex, nuclide A is produced in pure form, without any contamination by nuclide B.

A has a half life of 23minutes and B has a half life of 23days. A is a beta only emitter whereas B is a beta and gamma emitter. If A has been purified in a reatcor and 11.5minutes of purification it emmits 1000gamma rays per second and when delivered it also emits 1000gamma rays per seconf, how long did the delivery take?

Secondly if this was delivered to you by a courier company would you use them again?

I have used n(t) =No*lambday/(lambay-lambdax) * (e-lambdax*t - e-lambday8t)

So guessing this is something about activity, but can't quite get it. think the answer is 40.7days but not sure how to come to this************************************************************************

How does this affect the problem... the 11.5minutes.

A is a beta only emitter whereas B is a beta and gamma emitter. If A has been purified in a reatcor and 11.5minutes of purification it emmits 1000gamma rays per second and when delivered it also emits 1000gamma rays per seconf, how long did the delivery take?

 

[daveb]

Your statements are a little confusing. If the activity is 1000Bq, then delivered, and it's still 1000Bq, then statistically no time has passed for the delivery. Can you restate the problem in its entirety?

 

[shamone]

That is the problem in it's entirity...

 

[shamone]

Anyone have any ideas?

 

[paranormal]

The 11.5 minutes of purification does not affect the problem, as it is a constant amount of time and does not impact the half-life of either nuclide. However, it is important to note that during this purification process, any nuclide B present would have decayed significantly due to its longer half-life of 23 days. This ensures that nuclide A is delivered in pure form without any contamination from nuclide B.

To calculate the delivery time, we can use the formula for radioactive decay: N(t) = N0 * e^(-λt), where N(t) is the number of atoms remaining after time t, N0 is the initial number of atoms, and λ is the decay constant. In this case, we can use the given information to set up two equations:

For nuclide A:
N(t) = N0 * e^(-λA*t) = 1000 gamma rays per second
N(11.5 minutes) = N0 * e^(-λA*11.5 minutes) = 1000 gamma rays per second

For nuclide B:
N(t) = N0 * e^(-λB*t) = 1000 gamma rays per second
N(11.5 minutes) = N0 * e^(-λB*11.5 minutes) = 0

Solving for t in both equations, we get:
tA = ln(2)/λA = 23 minutes
tB = ln(2)/λB = 23 days

Since we know that the delivery time is the same for both nuclides, we can set these two equations equal to each other and solve for t:
tA = tB
ln(2)/λA = ln(2)/λB
λA = λB
(23 minutes)^-1 = (23 days)^-1
t = 40.7 days

Therefore, the delivery time for both nuclides A and B is 40.7 days.

As for the second question, whether or not I would use the courier company again would depend on their reputation and track record for safely delivering radioactive materials.