An accident at a UK nuclear reprocessing plant caused an area of local moor-land to be contaminated with the?

Question

An accident at a UK nuclear reprocessing plant caused an area of local moor-land to be contaminated with the radioactive isotope cobalt-60, which has a half-life of 5.23 years. The radioactivity of the moor-land just after the accident was measured at 500 bequerels.m-2.

Public access to the moor-land was restricted until the level of radioactivity
fell to 1.0 bequerel.m-2. How long must access be restricted ?

useful equation:

In {original activity / existing activity} = k x time taken.



Hint : First use the value of the half-life and the logarithmic relationship between radioactivity and time, given above, to determine k, the rate constant.

Now use the value of k obtained to predict the access restriction time.

Answer 1

rate of disintegration [proportional to] present
- dN/dt = k N >>> k = decay constant
dN/N = - kdt >>> log (N) = - kt + C
at t=0, N=No (max) = 500
---------
N = 500 e^-kt ------- (1)
-------------
N = No/2 during half life >> t = 5.23 year
(1/2) = (1/e^5.23k)
e^5.23k = 2 >>
k = (1/5.23) log(e) [2] = 0.1325 (1/year)
---------------------
N = 1 (unit) at t = t
1 = 500 e^-kt
e^kt = 500
kt = log (500)
t = [1/k] log 500 = 46.90 years

Answer 2

From equation given,

ln 2 = k x t(1/2)

Use this value of k in the same equation, apply now to your specific problem, to get your answer:

ln (500/1) = k x ln t

where t is what you are after.

That's all! Equations are a two-way street.

Answer 3

No it isnt. If another MEP/MP was allowed to visit Sellafield for the same purpose then it would be seen as a serious case of discrimination for political not security reasons.