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triac
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Homework Statement
A piece of Am-241 has a radioactivity of 10kBq. Determine how much Am-241 it contains.
Homework Equations
[tex]N(t)=N_0(\frac{1}{2})^{t/T_{1/2}} [/tex]
The Attempt at a Solution
Let A be the activity
Let N be the number of atoms
We know that [tex]A(t)=A_0(\frac{1}{2})^{t/T_{1/2}}[/tex] We can set our initial time to zero, which gives us [tex]A(t)=10kBq=A_0[/tex].
Furthermore, we know that A(t)=-N(t). We also know that [tex]N(t)=N_0(\frac{1}{2})^{t/T_{1/2}} => N'(t)=-\frac{N_0ln2}{T_{1/2}}(\frac{1}{2})^{t/T_{1/2}}[/tex][tex]=>N'(0)=-\frac{N_0ln2}{T_{1/2}}=10kBq => N_0=\frac{10kBqT_{1/2}}{ln2}[/tex]. Now we use that one atom weights 241,0568229u and that the half-life is 432,2 y (I converted it to seconds). Then we get that the mass of our "piece" is approximately 78,7 micrograms. However, in the key it says 1,83 ng.
What am I doing wrong here?