Question

If a 12.0-g sample of radon-222 decays so that after 19 days only 0.375 g remains, what is the half-life of radon-222? 9.50 days 4.75 days 3.80 days 0.594 days

Answer 1

3.80 Days

Look at the above comment for the math.

Answer 2

`A_(f)=A_(0)*(1/2)^{ (t)/(h)} A(f) - final amount, A(0) -initial amount,t - time, h- half-life. \\ \\0.375=12.0*(1/2)^{ (19)/(h)} \\ \\(0.375/12.0)=(1/2)^{ (19)/(h)} \\ \\log(0.375/12.0)=log(1/2)^{ (19)/(h)} \\ \\ (19)/(h)*log(1/2)= log(0.375/12.0) \\ \\ (19)/(h)= (log(0.375/12.0))/(log(1/2)) \\ \\ h= (19log(1/2))/(log(0.375/12.0)) =3.80 (days) \\ \\ h=3.80(days)`