Question

Answer is 1.25, but I am not sure how to do it

Radon-222 undergoes a decay (t1/2 3.8 days) to form polonium-218. How long will it take for 0.200 mol of polonium-218 to form from 1.00 mol of radon-222? (1) 1.25 days 2)1.00 days (3) 0.75 days (4) 0.90 days (5) 8.82 days

Answer 1

Randon-222 rightarrow polonium-218 For decay t = t_1/2/ln(2) ln (N_0 /N) Here t_1/2 = 3.8 days N_0 = initial amount of Randon-222 rightarrow N_0 = 1.00 mal N = amount of Randon-22 left at time t decay amount = amount of polonium-218 at time t = 0.200 mol N = N_0 -decay amount N = N_0 -0.200 mol N = 1.00 mol - 0.200 mol N = 0.800 mol t = time rightarrow t = ? t = t_1/2/ln (2) ln(N_0 /N) t = (3.8 days) /ln (2) ln (1.00 mol/0.800 mol) t = 1.22 days Closest option is 1.25 days.