The average activity of 40K in the human body is approximately 1.40 x 10^11 Bq.
The average activity of 40K in the human body can be estimated using the provided information about its abundance, half-life, and the total body potassium mass.
Here's how:
1. Calculate the number of 40K atoms in the body:
We know the average mass of potassium in the body is 140 g.
We also know the abundance of 40K in natural potassium is 0.0118%.
Therefore, the mass of 40K in the body can be calculated as:
Mass of 40K = (0.0118/100) * 140 g = 0.01652 g
Now, convert the mass to the number of atoms using Avogadro's number (6.022 x 10^23 atoms/mol) and the atomic mass of potassium (39.0983 g/mol):
Number of 40K atoms = (0.01652 g) * (6.022 x 10^23 atoms/mol) / (39.0983 g/mol) = 2.62 x 10^20 atoms
2. Calculate the decay constant:
The half-life of 40K is given as 1.28 x 10^9 years.
We can use the formula for radioactive decay to calculate the decay constant (λ):
λ = ln(2) / half-life = ln(2) / (1.28 x 10^9 years) = 5.38 x 10^-10 years^-1
3. Calculate the activity:
Activity (A) is the number of decays per unit time. It can be calculated using the formula:
A = λ * N
where N is the number of 40K atoms.
Therefore, the activity of 40K in the human body is:
A = (5.38 x 10^-10 years^-1) * (2.62 x 10^20 atoms) = 1.40 x 10^11 decays/s
4. Convert decays per second to Becquerel (Bq):
One Becquerel (Bq) is equal to one decay per second. Therefore, the activity in Bq is:
Activity = 1.40 x 10^11 decays/s * 1 Bq/decay = 1.40 x 10^11 Bq
Therefore, the average activity of 40K in the human body is approximately 1.40 x 10^11 Bq.
Question
The average mass of potassium in the human body is about 140 g. From the abundance and half-life given in Appendix D (0.0118% for 40K : T 1/2 = 1.28*10^9yr) , estimate the average activity of 40K in the body.