Question

You have just isolated a new radioactive element. If you can determine its half-life, you will win the Nobel Prize in physics. You purify a sample of 2 grams. One of your colleagues steals half of it, and four days later you find that 0.3 gram of the radioactive material is still left. What is the half-life? (Round your answer to three significant digits.)

Answer 1

staals half
1 gram left
0.3 grams left
half lives are normally written in years
it goes likt this


`A=P( (1)/(2))^ (t)/(h)`
A=final amount
P=initila amount
t=time elapsed
h=time half life is (same units as time)

let's use days as the units of time


we are given
initial amount=1gram
final amount=0.3gram
time=4 days

so

`0.3=1( (1)/(2))^ (4)/(h)`
solve for h

`0.3=( (1)/(2))^ (4)/(h)`
take the ln of both sides

`ln(0.3)=ln( (1)/(2))^ (4)/(h)`

`ln(0.3)=(4)/(h)ln( (1)/(2))`
times both sides by h

`hln(0.3)=4ln( (1)/(2))`
divide both sides by ln(0.3)

`h= (4ln( (1)/(2)) )/(ln(0.3))`
use calculator
h=2.30287
3 sig figs
h=2.303 days