The radioisotope, N-13, has a half-life of 10.0 minutes. What is the rate constant for the radioactive decay of N-13?

All radioactive decay follows of 1st order kinetics 

$C=c_0{e}^{-kt}$

$A=A_0{e}^{-\lambda t}$

$\lambda$: decay constant/distagration constant

t= time taken ; ${\mathrm{A}}_0$=initial activity 

${\mathrm{A}}_0$= number of nuclei present initially  

A= activity after time "t"

$\therefore$ Number of nuclei after time "t"

$\lambda$ : decay constant 

$\begin{array}{c}t{\phi }_2=10\min A=A0e^{-\lambda t}\\ \frac{A\sigma }{2}=A6e^{-\lambda t}\\ \frac{1}{2}=e^{-\lambda t}\ln \left(\frac{1}{2}\right)=-\lambda t_{{\psi }_2}\end{array}$

$\lambda =\frac{\ln 2}{10}\stackrel{-1}{min}$

$t0.693=-\lambda \left(10\right)$

$\lambda =0.0693 {\min }^{-1}$