Plz help. half-life

Question

Radium-223 decays with a half-life of 11.4 days.

How long will it take for a 0.240-mol sample of radium to decay to 7.50*10^-3 mol? 

Answer 1

First order decay.

FR = 0.5ⁿ

FR = fraction remaining = 7.50x10^-3 / 0.240 = 0.03125

n = number of half lives that have elapsed = ?

0.03125 = 0.5ⁿ'

log 0.03125 = n log 0.5

-1.505 = -0.301 n

n = 5 half lives have elapsed

Therefore ...

5 half lives x 11.4 days / half life = 57 days for the sample to decay to 7.5x10^-3 moles