# Calculating decay constants and half-life

1. Oct 26, 2008

### Steph191290

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.

2. Oct 26, 2008

### Hootenanny

Staff Emeritus
You might want to check the value of Avogadro's Constant

3. Oct 26, 2008

### Steph191290

oops that should have been 10^23 lol, thanks i'll try that
x

4. Oct 26, 2008

### Steph191290

now i get 1.4448x10^15 which is still wrong, im so confused.
x

5. Oct 26, 2008

### Hootenanny

Staff Emeritus
Your method is correct, you must just be punching the numbers into your calculator wrong. How many K atoms did you calculate?

6. Oct 26, 2008

### Steph191290

9.03x10^15
x

7. Oct 26, 2008

### Hootenanny

Staff Emeritus
Looks right to me.

8. Oct 26, 2008

### Steph191290

well i dont know what i did but i have just gotten the right answer thanks lol
xx

9. Oct 26, 2008

### Hootenanny

Staff Emeritus
As I said above, your method was spot on but you were probably just hitting the wrong buttons on your calculator.

10. Oct 26, 2008

### Steph191290

thanks lol, i do that alot it seems, better brush up on those skills before the exam lol.