Calculating decay constants and half-life

In summary, the scientist found that the decay constant for potassium is 1.8x10-17 and its half-life is 1.2x10^9years.
  • #1
Steph191290
30
0
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.



Homework Equations



decay constant = a/N
n=m/Mr

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, I am not sure wher to go from here any help would be appreciated.
 
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  • #2
You might want to check the value of Avogadro's Constant :wink:
 
  • #3
oops that should have been 10^23 lol, thanks i'll try that
x
 
  • #4
now i get 1.4448x10^15 which is still wrong, I am so confused.
x
 
  • #5
Steph191290 said:
now i get 1.4448x10^15 which is still wrong, I am 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?
 
  • #6
9.03x10^15
x
 
  • #7
Steph191290 said:
9.03x10^15
x
Looks right to me.
 
  • #8
well i don't know what i did but i have just gotten the right answer thanks lol
xx
 
  • #9
Steph191290 said:
well i don't 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.
 
  • #10
thanks lol, i do that a lot it seems, better brush up on those skills before the exam lol.
 

1. What is a decay constant and how is it calculated?

A decay constant is a measure of the rate at which a radioactive isotope decays. It is calculated by dividing the natural logarithm of 2 by the half-life of the isotope.

2. What is half-life and how is it related to decay constant?

Half-life is the amount of time it takes for half of the atoms in a sample of a radioactive isotope to decay. It is related to decay constant through the equation t1/2 = ln(2) / λ, where t1/2 is the half-life and λ is the decay constant.

3. How do I calculate the amount of a radioactive isotope remaining after a certain amount of time?

The amount of a radioactive isotope remaining after a certain amount of time can be calculated using the equation N = N0 * e-λt, where N is the amount remaining, N0 is the initial amount, λ is the decay constant, and t is the time elapsed.

4. What is the relationship between decay constant and the stability of an isotope?

The higher the decay constant of an isotope, the less stable it is. This means that it will decay at a faster rate compared to an isotope with a lower decay constant.

5. Is it possible for a radioactive isotope to have a decay constant of zero?

No, it is not possible for a radioactive isotope to have a decay constant of zero. All radioactive isotopes have some level of instability and will eventually decay, even if it takes a very long time.

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