Question 590776
A radioactive substance has a decay rate of 1.8% per year.
 What is its half life? Give your answer correct to 2 decimal places.
:
The radioactive decay formula: A = Ao*2^(-t/h), where
A = amt remaining after t time
Ao = initial amt; t-0
t = time of decay
h = half-life of substance
:
let initial amt = 1
then remaining amt = .982
let t = 1 yr
find h
:
1*2^(-1/h} = .982
Use natural logs
ln(2^(-1/h)) = ln(.982)
:
{{{-1/h}}} = {{{ln(.982)/ln(2)}}}
use your calc
{{{-1/h}}} = -.0262
-.0262h = -1
h = {{{1/.0262}}}
h ~ 38.17 yrs is the half-life
:
:
The radioactive element carbon-14 has a half-life of 5750 years.
 The percentage of carbon-14 present in the remains of plants and animals can be used to determine age.
 How old is a skeleton that has lost 44% of its carbon-14?
:
Find the remaining carbon if initial amt = 1: 1-.44 = .66
Find t
1*2^(-t/5750} = .66
Use natural logs
ln(2^(-t/5750)) = ln(.66)
:
{{{-t/5750}}} = {{{ln(.66)/ln(2)}}}
use your calc
{{{-t/5750}}} = -.59946
t = -5750 * -.59946
t = +3,447 years