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, we can use the formula:
Activity = Initial Activity * e^(-decay constant * time)
Given:
Initial Activity (A0) = 3.7x10^11 Bq
Activity after 4 hours (A) = 2.96x10^11 Bq
Time (t) = 4 hours
a) Decay Constant (λ):
To find the decay constant, we need to rearrange the formula:
decay constant = -(ln(A) - ln(A0)) / t
First, let's calculate the natural logarithm (ln) of A and A0:
ln(A) = ln(2.96x10^11 Bq)
ln(A0) = ln(3.7x10^11 Bq)
Now, substitute the values into the equation:
decay constant = -(ln(2.96x10^11 Bq) - ln(3.7x10^11 Bq)) / 4 hours
Using a calculator, subtract the natural logarithms and divide by 4 hours to find the decay constant.
b) Half-Life (T1/2):
The half-life can be calculated using the decay constant (λ):
half-life (T1/2) = ln(2) / decay constant
Substitute the value of the decay constant obtained in part a) into the equation:
half-life (T1/2) = ln(2) / decay constant
Using a calculator, divide the natural logarithm of 2 by the decay constant to find the half-life.
Note: Make sure to convert the time into the appropriate units (e.g., seconds, minutes, or days) if required.