Answer:
[tex]t \approx 50.4\,min[/tex]
Step-by-step explanation:
The time constant of the element X is:
[tex]\tau = \frac{13\,min}{\ln 2}[/tex]
[tex]\tau = 18.755\,min[/tex]
The decay function has the following form:
[tex]\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
[tex]t = -\tau \cdot \ln \frac{m}{m_{o}}[/tex]
[tex]t = -(13\,min)\cdot \ln \left(\frac{11\,g}{530\,g} \right)[/tex]
[tex]t \approx 50.4\,min[/tex]
