Question 253874
beryllium-11 decomposes into boron-11 with a half life of 13.8 seconds.
 How long will it take 240 g of beryllium-11 to decompose into 7.5g of beryllium-11?
:
Here is what it should be then:
2^(-t/13.8) = {{{7.5/240}}}
2^(-t/13.8) = .03125
:
Find the natural log of both sides
ln(2^(-t/13.8)) = ln(.03125)
:
log equiv of exponents
{{{-t/13.8}}}*ln(2) = ln(.03125)
:
{{{-t/13.8}}}(.693) = -3.4657
:
{{{-.693t/13.8}}} = -3.4657
:
Multiply both sides by -13.8
.693t = -13.8 * -3.4657
693t = +47.827 seconds
t = {{{(47.827)/(.693)}}}
t = 69 sec
:
:
Check on a calc: enter 240*2^(-69/13.8) = 7.500