Answer:
The number of days is approximately 8.
Step-by-step explanation:
Given : A medical scientist has a 15-gram sample of I-13, And would like to know it's half-life in days. he also knows that k=0.0856.
To find : The half-life, in days, of I-131 using the information at the left?
Solution :
The decay model is given by [tex]N=N_0e^{-Kt}[/tex]
We have given that,
The substance's half-life is the time it takes for the substance to decay to half its original amount.
i.e. [tex]N=\frac{N_0}{2}[/tex]
The value of k is k=0.0856.
Substitute the values in the formula,
[tex]N=N_0e^{-Kt}[/tex]
[tex]\frac{N_0}{2}=N_0e^{-(0.0856)t}[/tex]
[tex]\frac{1}{2}=e^{-(0.0856)t}[/tex]
Taking natural log both side,
[tex]\ln\frac{1}{2}=\ln e^{-(0.0856)t}[/tex]
[tex]-\ln2=-(0.0856)t\ln e[/tex]
[tex]t=\frac{-\ln2}{-0.0856}[/tex]
[tex]t=8.09[/tex]
Therefore, The number of days is approximately 8.
