Question

Chromium-51 has a half life of 27.70 days. How much will be left after 166.2 days if

Answer 1

Answer:

Decayed mass: 909.56 g, Left mass: 14.44 g.

Explanation:

The time constant of the Chromium-51 is:

$\tau = \frac{t_{1/2}}{\ln 2}$

$\tau = \frac{27.70\,days}{\ln 2}$

$\tau = 39.963\,days$

The decay equation for the isotope has the following form:

$\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }$

The total decay at a given instant t is:

$\% \delta = \left(1-e^{-\frac{t}{\tau} } \right) \times 100\,\%$

The total decay at 166.2 days is:

$\% \delta = 98.437\,\%$

Decayed mass: 909.56 g, Left mass: 14.44 g.