Answer:
Decayed mass: 909.56 g, Left mass: 14.44 g.
Explanation:
The time constant of the Chromium-51 is:
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex]
[tex]\tau = \frac{27.70\,days}{\ln 2}[/tex]
[tex]\tau = 39.963\,days[/tex]
The decay equation for the isotope has the following form:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
The total decay at a given instant t is:
[tex]\% \delta = \left(1-e^{-\frac{t}{\tau} } \right) \times 100\,\%[/tex]
The total decay at 166.2 days is:
[tex]\% \delta = 98.437\,\%[/tex]
Decayed mass: 909.56 g, Left mass: 14.44 g.
