A 73-kg person is accidentally exposed for 215 s to a 16-mCi source of beta radiation coming from a sample of 14C.
What is the activity of the radiation source in disintegrations per second? In becquerels?
i am not sure if there is an equation for this or wut??
To calculate the activity of the radiation source in disintegrations per second and becquerels, you need to use the decay constant and the definition of activity.
1. First, we need to convert the activity of the radiation source from millicuries (mCi) to curies (Ci). Since 1 Ci is equal to 1000 mCi, we have:
16 mCi = 16/1000 Ci = 0.016 Ci
2. The decay constant (λ) for a radioactive isotope can be determined using the half-life (t½) of that isotope. For 14C, the half-life is approximately 5730 years. We can convert this to seconds by multiplying by the number of seconds in a year (365 days * 24 hours * 60 minutes * 60 seconds):
t½ = 5730 years * 365 days * 24 hours * 60 minutes * 60 seconds = 1.808 × 10^11 seconds
3. The decay constant (λ) can be calculated using the following equation:
λ = 0.693 / t½
λ = 0.693 / 1.808 × 10^11 seconds
4. Now, we can calculate the activity (A) using the formula for activity:
A = λ * N
where N is the number of radioactive nuclei.
To determine N, we need to know the number of moles of the radioactive isotope, which can be calculated using the mass and molar mass of the element.
5. 14C has a molar mass of approximately 14 g/mol. Since the person's mass is given as 73 kg, we can find the number of moles (n) using the equation:
n = mass / molar mass
n = 73 kg / 14 g/mol = 5.214 mol
6. The number of radioactive nuclei (N) is given by Avogadro's number (6.02214076 × 10^23 atoms/mol) multiplied by the number of moles (n):
N = Avogadro's number * n
N = 6.02214076 × 10^23 atoms/mol * 5.214 mol
7. Now we can calculate the activity in disintegrations per second:
A (disintegrations per second) = λ * N
8. Finally, to convert the activity to becquerels (Bq), we multiply the value obtained from step 7 by 3.7 × 10^10, as 1 curie is equal to 3.7 × 10^10 becquerels.
A (Bq) = A (disintegrations per second) * 3.7 × 10^10
By following these steps and plugging in the values, you can calculate the activity of the radiation source in both disintegrations per second and becquerels.