# Homework Help: Proving the half-life of Potassium-40

1. Mar 18, 2013

### GandhiReborn

1. The problem statement, all variables and given/known data

"K-40... decays by two radioactive processes. It can decay by electron capture or β- emission.

It is found that a sample containing 4.0x10^18 nuclei of K-40 emits a total of 68 β- particles and photons each second. This shows the half life is 1.3x10^9 years."

Use the data in the passage to show that the half life is 1.3x10^9 years.

2. Relevant equations

I'm assuming...

T1/2 = ln2/λ; A=λN; A=A0e^(-λ)(t)

3. The attempt at a solution

Using A=λN --> A/N=λ --> (68)/(4*10^18) = 1.7^10-17
then ln2/(1.7^10-17) = 4.1*10^16 ->> waayy too big.

I then tried various other combinations of the above, but to no success.

Please help!! I know I'm missing something VERY obvious.

2. Mar 18, 2013

### phyzguy

You calculated (correctly) the half-life in seconds. Now convert to years.

3. Mar 18, 2013

### GandhiReborn

D'oh!!!!!!!!!!!!

You legend, thank you :D

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