Verifying 226-Ra Half-Life Calculation

[Prometium]

Homework Statement

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?

Homework 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

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?

 

[haruspex]

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

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