SOLUTION: 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?
based on the forumu
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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?
based on the forumula provided in the text book C(t)=C(0)2e^-t/h
where C(0) = 240, C(t)=7.5 ,h=13.8
7.5/240=2e^-t/13.8
this was a s far as i got
Found 3 solutions by ankor@dixie-net.com, Theo, martin.jabou:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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) =
2^(-t/13.8) = .03125
:
Find the natural log of both sides
ln(2^(-t/13.8)) = ln(.03125)
:
log equiv of exponents
*ln(2) = ln(.03125)
:
(.693) = -3.4657
:
= -3.4657
:
Multiply both sides by -13.8
.693t = -13.8 * -3.4657
693t = +47.827 seconds
t =
t = 69 sec
:
:
Check on a calc: enter 240*2^(-69/13.8) = 7.500
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your equation to work with is:
The exponent in the equation is .
substituting in that equation, you get:
the exponent in the equation is
you want to isolate the exponential term on the right hand side of the equation so you need to divide both sides of the equation by 240 * 2 to get:
the exponent in the equation is
take the log of both sides of this equation to get:
since log(b^c) = c*log(b), your equation becomes:
multiply both sides of this equation by 13.8 to get:
divide both sides of this equation by -log(e) to get:
solve for t to get:
seconds.
substitute in original equation to see if this value for t is good.
original equation is:
exponent in the equation is
t = 57.39258655
equation becomes:
exponent in the equation is
simplify to get:
simplify further to get:
since the equation is true, the value for t is good.
t = 57.39258655 seconds
Answer by martin.jabou(1) (Show Source): You can put this solution on YOUR website!
The solution is quite simple actually:
You know you are going from 240g of Be-11 to 7.5g of Be-11, so write down what you have -
Half Life Formula is C(t) = Cø2^(-t/H)
C(t) = 7.5g, Cø = 240g, H = 13.8 seconds
Sub In:
7.5 = 240 (2)^(-t/H)
Divide both sides by 240 to get:
7.5 / 240 = 2^(-t/13.8)
Simplify:
1 / 32 = 2^(-t/13.8)
1 / 32 must be written as a base two: therefore it becomes 2 ^ -5, your new equation is:
2^-5 = 2^(-t/13.8)
Since at this point you have the same base 2 on both sides, you can now equate the exponents to each other and solve for variable t. You get:
-5 / 1 = -t/13.8
-69 = - t, divide each side by -1 (not particularly necessary since we know time cannot be negative) and we get T is equal to 69 seconds :)
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