A newly prepared radioisotope has activity 3.7x10^11 Bq. After 4 hours, its activity is reduced to 2.96x10^11.calculate
a) decay constant
b) its half life
To calculate the decay constant and the half-life of a radioactive isotope, we can use the decay equation:
A = A0 * e^(-λt)
Where:
A = final activity
A0 = initial activity
λ = decay constant
t = time
Given:
A0 = 3.7x10^11 Bq
A = 2.96x10^11 Bq
a) To calculate the decay constant (λ), we can rearrange the equation:
λ = -ln(A/A0) / t
Substituting the given values:
λ = -ln(2.96x10^11 Bq / 3.7x10^11 Bq) / 4 hours
Calculating this using a scientific calculator or software, we find:
λ ≈ 0.0986 hours^(-1)
b) To calculate the half-life (T1/2), we can use the following equation:
T1/2 = ln(2) / λ
Substituting the value of λ we found earlier:
T1/2 = ln(2) / 0.0986 hours^(-1)
Calculating this, we find:
T1/2 ≈ 7.02 hours
Therefore, the decay constant is approximately 0.0986 hours^(-1) and the half-life is approximately 7.02 hours.