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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 :

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

[tex]A=P( \frac{1}{2})^ \frac{t}{h} [/tex]
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
[tex]0.3=1( \frac{1}{2})^ \frac{4}{h} [/tex]
solve for h
[tex]0.3=( \frac{1}{2})^ \frac{4}{h} [/tex]
take the ln of both sides
[tex]ln(0.3)=ln( \frac{1}{2})^ \frac{4}{h} [/tex]
[tex]ln(0.3)=\frac{4}{h}ln( \frac{1}{2})  [/tex]
times both sides by h
[tex]hln(0.3)=4ln( \frac{1}{2})  [/tex]
divide both sides by ln(0.3)
[tex]h= \frac{4ln( \frac{1}{2}) }{ln(0.3)} [/tex]
use calculator
h=2.30287
3 sig figs
h=2.303 days

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