Question

The half-life of 235U, an alpha emitter, is 7.1×108 yr.

Part A Calculate the number of alpha particles emitted by 3.4 mg of this nuclide in 3 minutes. Express your answer using two significant figures.

Answer 1

answer: 1.3*10^19

first order kinetics,

k = 0.693/t1/2

   = 0.693/(7.1*10^8)

   = 9.76*10^-10 y-1

k = (1/t)ln(a/x)

a = initial amount = 3.4 mg

x = amount of isomer after t, time = x mg

t= time = 3 min

(9.76*10^-10*365*24*60) = (1/3)ln(3.4/x)

x = 3.3948 mg

no of mol of 235-U disintegrated = (3.4-3.3948)/235 = 2.213*10^-5 mol

no of mol of alpha particel released = 2.213*10^-5 mol

no of alpha particel released = 2.213*10^-5*6.023*10^23

               = 1.3*10^19