Question

I need some help figuring this one out and how to do it.

14.) One isotope of the radioactive element thorium is 227th, which undergoes a-decay according to the equation: 227Th → 223Ra + a. If the half-life of 227Th is 18.7 days, what is the rate of a- particle production, in a.s., from a sample of 510 ug of 22 Th? 227Th 227.0277 g.mol a. 5.0x1016 a:s! b. 5.8x1011 a.s -1 c. 5.8*108 a-s-1 d. 1.0x1012 a.s?

Answer 1

Answer: b. 5.8*10^11 x*s-1

rate constant(k) = 0.693/t1/2

t1/2 = half life time = 18.7 days

k = 0.693/(18.7*24*60*60) = 4.29*10^-7 s-1

no of mol of 227Th sample taken = 510*10^-6 / 227.0277 = 2.25*10^-6 mol

no of particles of 227Th sample taken = (2.25*10^-6)*(6.023*10^23)

                                      = 1.355*10^18 particles

from equation , 1 mol 227Th = 1 mol alpha(x) particle

no of alpha particles of produced = 1.355*10^18 particles

rate = k*no of particles

     = 4.29*10^-7*1.355*10^18

     = 5.8*10^11 x*s-1