Question

Direction: Solve the following problems. Show your solution and use the appropriate number of significant figures.

1.Problem(20 points):Radon-222 has a half-life of 3.8 days. The source water for drinking water treatment plant contains 1250 μmol/L of radon. How long must the water be stored to meet the US EPA limit of 300 μmol/L?

Answer 1

Answer: 7.82 days

Solution:

$N=N_{0}×(1/2)^{\frac{t}{T_{1/2}}}$

$\ln{\frac{N}{N_{0}}}=-{\frac{t}{T_{1/2}}}×\ln2$

$t=-\frac{\ln{\frac{N}{N_{0}}}×{T_{1/2}}}{\ln2}=-\frac{\ln{\frac{C}{C_{0}}}×{T_{1/2}}}{\ln2}$

$t=-\frac{\ln{\frac{300\,\mu mol/L}{1250\,\mu mol/L}}×{3.8\,days}}{\ln2}=7.82\,days$