Answer: The amount of time needed is 4.53 minutes.
Explanation:
The equation used to calculate time period follows:
[tex]\ln A=\ln A_o-kt[/tex]
where,
[tex]A_o[/tex] = initial mass of Cr-56 isotope = 34.5 mg
A = mass of the Cr-56 isotope left after the time = 20.3 mg
t = time = ? min
k = rate constant = [tex]1.17\times 10^{-1}min^{-1}[/tex]
Putting values in above equation, we get:
[tex]\ln (20.3)=\ln (34.5)-[(1.17\times 10^{-1}min^{-1})\times t]}\\\\t=\frac{\ln(34.5)-\ln(20.3)}{1.17\times 10^{-1}}=4.53min[/tex]
Hence, the amount of time needed is 4.53 minutes.
