Question

15.58 The half-life for the radioactive decay of C−14 is 5730 years. How long will it take for 25% of the C−14 atoms in a sample of C−14 to decay? If a sample of C−14 initially contains 1.9 mmol of C−14, how many millimoles will be left after 2250 years?

Answer 1

Given, T_1/2=5730 years

k=0.693/T_1/2=0.693/5730=1.209*10^-4 years^-1

For 25% to decay,

X_A=0.25

ln(1-X_A)=-kt

ln(1-0.25)=-1.209*10^-4*t

t=2380 years

For millimoles remaining after t=2250 year

ln(1-X_A)=-1.209*10^-4*2250

1-X_A=0.762

Moles remaining=initial moles(1-X_A)

                                =1.9 mmol*0.762

                                =1.45 milli moles