Radioactive decay is a process that follows 1st order kinetics. The half-life decay for Cs-133 is 15,300 years, and for Cs-135 is 56 years?

Question

The rate law is Rate = k(N) where N is the number of nuclei that decompose per unit of time.

a) Calculate the rate constant for the decay of Cs-133 and Cs-135

b) If one starts with 3.2 grams of pure Cs-135, how many nuclear disintegrations per-second occur initially?

c) What mass of Cs-135 is left after 1.0 year, 10. years, and 100 years?

hcbiochem · Answer

a) Rate constant(Cs-133) = ln 2 / t1/2 = 0.693 / 15300 yr = 4.53X10^-5 yr^-1
Rate constant (Cs-135) = 0.693 / 56 yr = 0.0124 yr^-1

b) Number nuclei = 3.2 g / 135 g/mol X 6.022X10^23 = 1.43X10^22 nuclei
Activity = 0.693 N / t1/2 
Activity = 0.693 (1.43X10^22) / 56 yr = 1.77X10^22/yr X (1 yr / 3.154X10^7 s) = 5.6X10^12 disintegrations/second

c) ln N = -kt + ln No
ln N = -0.0124 yr-1(1.0 yr) + ln 3.2 g
N = 3.16 g

ln N = -0.0124 yr-1(10 yr) + ln 3.2 g
N = 2.83 g

ln N = -0.0124 yr-1(100 yr) + ln 3.2 g
N = 0.93 g

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Radioactive decay is a process that follows 1st order kinetics. The half-life decay for Cs-133 is 15,300 years, and for Cs-135 is 56 years?

1 Answer