Calculating activity using half life

[Kira127]

The question is that the human body contains 0.2% potassium by weight and the natural abundance of 40K is 0.0118%. The half life of 40K is 1.28x10^9 years and I have to calculate the activity in an adult weighing 75 kg. What I tried was to find the decay constant by 0.693/1.12x10^13 hours = 6.18x10^-14. Then I took the mass and divided it by the 40K 14.11kg/40 * 6.02x10^23 = 2.12 x10^23. Then I tried Activity=lambda*N =6.18x10^-14*2.12x10^23=1.31x10^10. The answer is supposed to be 4.39x10^-6 and I don't know what I'm doing wrong if someone could help me that would be very much appreciated.

 

[phyzguy]

A couple of questions:

(1) If you weigh 75kg, and 0.2% of that is K, and 0.0113% of THAT is K40, do you really think there are 14kg of K40 in your body?

(2) Do you really want the time constant in 1/hr?

(3) If you think the final answer is 4.39E-6, what are the units of that?

 

[raining Pete]

Hi there,

It looks like you are on the right track with your calculations, but there are a few things you might have missed or calculated incorrectly.

First, when finding the decay constant, you need to use the half-life in seconds, not hours. So the correct calculation would be 0.693/1.12x10^13 seconds = 6.18x10^-17.

Next, when finding the number of 40K atoms in the body, you need to use the fraction of 40K in the body (0.0118%), not the mass. So the correct calculation would be 75kg * 0.0118% * 6.02x10^23 = 5.31x10^20 atoms.

Finally, when calculating the activity, you need to use the number of decays per second, not the number of atoms. So the correct calculation would be 6.18x10^-17 * 5.31x10^20 = 3.28x10^4 decays per second.

To convert this to the desired units of Becquerels (Bq), you need to divide by the number of seconds in a year (3.15x10^7). So the final answer would be 3.28x10^4 Bq, which is equivalent to 3.28x10^-1 mBq or 3.28x10^-6 uBq.

I hope this helps clarify the steps and calculations needed. Keep up the good work!