Nuclear physics - decay constant

[shahar weiss]

Homework Statement

Hello.
Im having a problem here, i got a sample of Au nucleis.
I'm bombing them with neutrons and each second 20^10 of them undergo a reaction where they turn radioactive.
Im trying to look at this problem as if i would have a sample of radioactive materia which decaying to something else.
Now if i do so, then the activity of my sample (A) is 20^10 disintegration/second which is constant.
im trying to figure out my "decay constant" and the half life time. for that ill define that at t=0 i have K(number) of radioactive nucleins.
i have a few formulas for A.
A(t) =(def) dN/dT = N(t) = e^(-[tex]\lambda[/tex]t)
since A is constant, then A(T)=A(0)=20^10.
but if ill put this is the equation above i will lose t.. anyway I am really lost here and i would be so happy for help.
thank you very to whoever helps me out

Homework Equations

A(t) =(def) dN/dT = N(t) = e^(-[tex]\lambda[/tex]t)

The Attempt at a Solution

Again as mentioned above, trying to use this formula, won't work

 

[jbsteele]

as it will give you an equation with no t. To solve this problem, you need to use the following formula:A(t) = A(0)*e^(-\lambdat)where A(0) is your initial activity, and \lambda is your decay constant.Solving for \lambda gives you: \lambda = -ln(A(t)/A(0))/tNow all that is left is to plug in your values for A(t) and A(0). So, \lambda = -ln(20^10/20^10)/t = 0/t, therefore \lambda = 0And since \lambda = 0, then the half-life of your sample is infinite.