Question

Part c if you accidentally spill phosphorus-32 onto your shoe, how long would it take before 99.9% of the radioactive material has decayed so that you can safely wear the shoes again? express your answer as an integer. view available hint(s)

Answer 1

Answer:

$t \approx 142.514\,days$

Step-by-step explanation:

The half-life of the phosphorus-32 is 14.3 days. The time constant of the isotope is:

$\tau = \frac{14.3\,days}{\ln 2}$

$\tau = 20.631\,days$

The decay formula is:

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

The time related to the decayed proportion of the radioactive isotope is:

$-\frac{t}{\tau} = \ln \left(\frac{m}{m_{o}} \right)$

$t = -\tau \cdot \ln \left(\frac{m}{m_{o}} \right)$

$t = - (20.631\,days)\cdot \ln 0.001$

$t \approx 142.514\,days$