Calculating decay constants and half-life


by Steph191290
Tags: constants, decay, halflife
Steph191290
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#1
Oct26-08, 06:39 AM
P: 30
A scientist wishes to find the age of a sample of rock. Realising that it contains radioactive potassium, which decays to give a stable form of argon, the scientist started by making the following measurments:

decay rate of the potassium in the sample = 0.16Bq
mass of potassium in the sample = 0.6x10^-6g
mass of argon in the sample = 4.2x10^-6g

The Molar mass of the potassium is 40g. show that the decay constant for potassium is 1.8x10-17 and its half-life is 1.2x10^9years.



2. Relevant equations

decay constant = a/N
n=m/Mr

3. The attempt at a solution


N=m/Mr
N=0.6x10^-6/40
N=1.5x10^-8

N=1.5x10^-8 x 6.02x10^-8
N=9.03 x 10^-16

decay constant = a/N
decay constant = 0.16/9.03x10^-16

I got this far then got stck as the answer was wrong, im not sure wher to go from here any help would be appreciated.
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Hootenanny
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#2
Oct26-08, 07:02 AM
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You might want to check the value of Avogadro's Constant
Steph191290
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#3
Oct26-08, 08:18 AM
P: 30
oops that should have been 10^23 lol, thanks i'll try that
x

Steph191290
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#4
Oct26-08, 08:29 AM
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Calculating decay constants and half-life


now i get 1.4448x10^15 which is still wrong, im so confused.
x
Hootenanny
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#5
Oct26-08, 08:37 AM
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Quote Quote by Steph191290 View Post
now i get 1.4448x10^15 which is still wrong, im so confused.
x
Your method is correct, you must just be punching the numbers into your calculator wrong. How many K atoms did you calculate?
Steph191290
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#6
Oct26-08, 08:39 AM
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9.03x10^15
x
Hootenanny
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#7
Oct26-08, 08:49 AM
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Quote Quote by Steph191290 View Post
9.03x10^15
x
Looks right to me.
Steph191290
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#8
Oct26-08, 08:53 AM
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well i dont know what i did but i have just gotten the right answer thanks lol
xx
Hootenanny
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#9
Oct26-08, 08:54 AM
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Quote Quote by Steph191290 View Post
well i dont know what i did but i have just gotten the right answer thanks lol
xx
As I said above, your method was spot on but you were probably just hitting the wrong buttons on your calculator.
Steph191290
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#10
Oct26-08, 08:56 AM
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thanks lol, i do that alot it seems, better brush up on those skills before the exam lol.


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