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 substanc
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To calculate the activity (A) of potassium-40 (K-40) in the average human body, we need to use its half-life (t1/2) and the given amount of potassium (K) in grams.
The half-life of potassium-40 is approximately 1.251 billion years (1.251 x 10^9 years). We can convert this into seconds by multiplying it by the number of seconds in a year: t1/2 = 1.251 x 10^9 years x 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute.
Now, let's convert the given amount of potassium (K) in grams into moles. The molar mass of potassium is approximately 39.1 g/mol. Therefore, we can calculate the number of moles (n) of potassium-40 in the body by dividing the mass of potassium (K) by its molar mass.
n = 1.4 x 10^2 g / 39.1 g/mol
Next, we need to calculate the decay constant (λ), which is the reciprocal of the half-life (λ = ln(2) / t1/2). This tells us how fast the radioactive substance (potassium-40) decays.
λ = ln(2) / (1.251 x 10^9 years x 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute)
With the decay constant (λ), we can now calculate the activity (A) in disintegrations per year. Activity is defined as A = λ * N, where N is the number of atoms.
N = n * Avogadro's number
= n * 6.022 x 10^23 atoms/mol
A = λ * N
= λ * (n * 6.022 x 10^23 atoms/mol)
Now we can substitute the values into this equation to get the activity in disintegrations per year for the average human body.