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.