The average human body has 1.4x10^2 g of total K within it. Calculate the activity in disintegration/year of the potassium-40 in the average human body using your value of t1/2 (or K) of this substance
To calculate the activity of potassium-40 (K-40) in the average human body, we need to use the equation for radioactive decay:
Activity = λ * N
Where:
- Activity is the rate of decay, measured in disintegrations per unit of time (in this case, per year).
- λ (lambda) is the decay constant.
- N is the number of radioactive atoms present.
First, let's find the decay constant (λ) for K-40. The half-life (t1/2) of K-40 is approximately 1.25 billion years. The decay constant can be calculated using:
λ = ln(2) / t1/2
λ = ln(2) / 1.25 billion years
Next, we need to calculate the number of radioactive K-40 atoms (N) in the average human body. We are given that there is 1.4x10^2 grams of total K (potassium) in the average human body. The molar mass of potassium (K) is approximately 39.10 g/mol, and the natural abundance of K-40 is about 0.012%.
To determine the number of K-40 atoms, we follow these steps:
Step 1: Convert the weight of K in grams to moles.
Number of moles = mass / molar mass
Step 2: Calculate the moles of K-40 atoms within the given mass.
Number of K-40 atoms = (number of moles) * (Avogadro's number) * (natural abundance of K-40)
Finally, we can substitute the values of λ and N into the activity equation to find the activity of K-40.
Note: Avogadro's number = 6.022 × 10^23
Let's go ahead and calculate the activity in disintegrations/year:
1. Calculate λ using the value of t1/2:
λ = ln(2) / 1.25 billion years
2. Determine the number of K-40 atoms:
a. Convert the weight of K to moles.
Number of moles = 1.4x10^2 g / 39.10 g/mol
b. Calculate the moles of K-40 atoms.
Number of K-40 atoms = (number of moles) * (Avogadro's number) * (0.012%)
3. Substitute the values of λ and N into the activity equation:
Activity = λ * N
This will give us the activity of K-40 in disintegrations/year in the average human body.