How Many Half-Lives Are Needed for Specific Decay Percentages?

[Sarah88]

Homework Statement

How many half-lives must elapse until (a) 90% and (b) 99% of a radioactive sample of atoms has decayed?

Homework Equations

N=No(1/2)^(t/t1/2)
N=No(1/2)^(n)

The Attempt at a Solution

The part of the solution I don't understand is how to get the second equation N=No(1/2)^n from N=No(1/2)^(t/t1/2). In other words, why is t/t1/2 grouped into the variable "n" if we don't know the value for t or the half life? Thank you!

 

[Borek]

Question asks about "how many half lives", t/t_1/2 is just that - number of half lives.

 

[ehild]

The number of half-lives (n) is the question. You do not know the half life, but you can calculate n from the ratio of N/No.

ehild

 

[Sarah88]

Ok, that makes a lot more sense, thank you!