The half of 14C isotope is 5730 year .if a sample of 14C contains 10^22 nuclei , what is the activity of the sample
The activity of a radioactive sample is given by:
Activity = decay constant x number of nuclei
The decay constant (λ) for 14C isotope can be calculated using the half-life formula:
t½ = ln(2) / λ
where t½ is the half-life and ln is the natural logarithm.
Substituting the given values, we get:
5730 years = ln(2) / λ
Solving for λ, we get:
λ = ln(2) / 5730 years
λ = 1.21 x 10^-4 year^-1
Now, we can calculate the activity of the sample:
Activity = (1.21 x 10^-4) x (10^22)
Activity = 1.21 x 10^18 decays per second (Bq)
Therefore, the activity of the sample is 1.21 x 10^18 Bq.
To determine the activity of the sample, we need to calculate the decay constant (λ) and use it in the formula for activity (A).
The decay constant can be found using the half-life (t1/2):
λ = ln(2) / t1/2
Substituting the given half-life of 14C (5730 years):
λ = ln(2) / 5730
Now, we can calculate the activity using the formula:
A = λ * N
Where N is the number of nuclei in the sample. Given N = 10^22:
A = (ln(2) / 5730) * (10^22)
Calculating this expression should give us the activity of the sample.