# Becquerel counting

1. Jun 28, 2013

### Prometium

1. The problem statement, all variables and given/known data

I think I'm very right om this assignment, but I would like to completely sure - so I'm thankful if someone educated in nuclear physics can check that this is correct.

226-Ra has a half-life of 1600 years. One source of radiation contains 1.0 mg of this Radium nuclide. What activity is there from this source of radiation about 5000 years?

2. Relevant equations

Half life: N(t) = N(0)*2^(-t/T1/2) But I prefer: N(t) = N(0)*0.5^(t/T1/2)

Acivity: Bq = (m/ma)NA(ln(2)/T1/2)

Atomic mass for Ra-226: 226.0254098 u

Seconds within 1600 years: 5.04576*10^10 s

3. The attempt at a solution

First, I was just answering in mg:

1.0*0.5^(5000/1600) = 0.1146255054 mg --> This is in grams: 1.146255054*10^-4 g

And yes, this is the amount of the source left after 5000 years - but not the acitivity. Please correct me if I'm wrong.

So now I just plug this in this amount in grams in this equation:

(m/ma)NA(ln(2)/T1/2)

Which is:

(1.146255054*10^-4) / (226.0254098)*NA*(ln(2)/(5.04576*10^10)) = 4'195'404.564 Bq

My result is: 4.2 MBq

Is completely this correct?

2. Jun 28, 2013

### haruspex

The equation looks right. I get slightly less.. 4.18E6.