# Half life questions

#### dev-hud

i am taking upgrading, and one of the main reasons i failed physics 30 to start with was due to half life. the book cant explain it good enough to me and either could my teacher. so i have a few questions that i would appreciate a starting point for.

How much time elapses before 90% of the radioactivity of a sample of 72/33As dissapears as measured by its activity? the half life is 26h.

A sample of radioactive material contains 10^15 atoms and has an activity of 6.00 x 10^11 Bq. What is the half life?

these are just a couple of the many questions i am struggling with.

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#### RoyalCat

$$N(t)=N_0 e^{-t/\tau}$$

Is all you need to know, along with the definition that the half life is the time it takes for half a given sample to decay.

After a time $$t=t_{1/2}$$ it holds that: $$N(t)=\tfrac{1}{2}N_0$$

Looking at the general form, we find that:
$$\tfrac{1}{2}=e^{-t_{1/2}/\tau}$$

Some algebra provides: $$\tau = \frac{t_{1/2}}{\ln{2}}$$

Now try and solve the problems and show us where you have difficulty.

#### AC130Nav

$$N(t)=N_0 e^{-t/\tau}$$

Is all you need to know, along with the definition that the half life is the time it takes for half a given sample to decay.

After a time $$t=t_{1/2}$$ it holds that: $$N(t)=\tfrac{1}{2}N_0$$

Looking at the general form, we find that:
$$\tfrac{1}{2}=e^{-t_{1/2}/\tau}$$

Some algebra provides: $$\tau = \frac{t_{1/2}}{\ln{2}}$$

Now try and solve the problems and show us where you have difficulty.
Don't feel bad if you don't agree that logarithmic manipulations aren't algebraic, I don't either. Doesn't mean they don't work.