# Difficult Nuclear Decay Qs

Tc-99 emits gamma rays of 140keV and has a half life of 6 hours. A patient is injected with Tc-99 of activity 4x10^6 Bq. Calculate the time taken for total gamma ray emission to be 1x10^-8J
Sorry you didn't get any replies. Here's a few equations that might help you a bit...

Unparseable latex formula:

[br]\begin{align*}[br]\textrm{P(t)} = \textrm{E_1}\times{\textrm{A(t)}} \\[br]\textrm{A(t)} = -\displaystyle\frac{d\textrm{N(t)}}{dt} \\ [br]\textrm{E_\Sigma(t)} = \displaystyle\int_0^t \textrm{P(t)} [br]\end{align*}[br]

The first eq is the power emitted by the source (given by the energy per emission multiplied by the activity, an implicitly positive quantity, given that the total amount of source, $N$, decays monatonically with time.) This is the bit that they expect you to figure out.

I know it looks nasty but it really isn't- just state the forms for each equation (you will have covered them at A-Level/A2) and you can easily solve it.

The second eq is the activity (directly covered in A2, if I recall, at least in AQA.)

The third eq is the total energy emitted, given by a simple integral of the power.
(edited 1 year ago)