Question

You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 3 days later you determine that it has decayed down to 0.6 grams. What is its half-life?

Answer 1

find how many half lives have passed

seems we are measuring in days

half life formula is as follows

`A=P((1)/(2))^(t)/(h)`
A=final amount
P=initial amount
t=time in a certain units (this time, it's days)
h=time of half life


so
we are given that P=1, A=0.6, t=3
find h
subsitute

`0.6=1((1)/(2))^(3)/(h)`

`0.6=((1)/(2))^(3)/(h)`
take ln of both sides

`ln(0.6)=ln(((1)/(2))^(3)/(h))`

`ln(0.6)=((3)/(h))ln((1)/(2))`
multiply both sides by h

`(h)ln(0.6)=3ln((1)/(2))`
divide both sides by ln(0.6)

`h=(3ln((1)/(2)))/(ln(0.6))`
use your calculator
h≈4.07075
so about 4 days is the half life