Question

A radioactive substance has a half life of 4 months,1/4

Answer 1

When in doubt, go back to definitions. What is a half life? It's the time it takes for half of a substance to decay.

If A0 is your initial amount, then after one half life, you'll have 12AO. After n half lives, you'll have (12)n.

Now, how many half lives do you have after t units of time? Well that would just be tth where th is the half life.

So we have A=Ao(12)tth.

So now all you have to do is work backwards. Solving for t, you get

t=thln(AA0)ln(12), if I didn't mess up any algebra.

Alternatively, you could think about this intuitively. If 34 decayed, then that means that only one quarter is left. How many half lives does that take? Well, after one half life, you have 12 of the original. After another half life, you have 1212=14. So two half lives have passed.

Hope u can now understand after reading this..

Thanku for reading my answer.