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## Homework Statement

A parent isotope has [tex]\tau_\frac{1}{2}=\delta[/tex]. Its decays through a series of daughters to a final stable isotope. One of the daughter particles has the greatest half life of [tex]\tau_\frac{1}{2}=\alpha[/tex]-- the others are less then a year. At t=0 the parent nuclei has [tex]N_0[/tex] nuclei, no daughters are present.

How long does it take for the population with the greatest half life to reach 97% its equilibrium value?

At some t, how many nuclei of the isotope with the greatest half life are present, assume no branching.

## Homework Equations

[tex]\frac{dN}{dt}=e^{-\lambda t}[/tex]

## The Attempt at a Solution

So for the first one:

Its just solving the diff eq above right? The daughter is in its eq. value or do we have to worry about decay from the other daughters?

the second one:

Basically plugging in t right for the solved diff eq with initial nuclei right?

Just checking, I feel like I'm missing something.