1. Radioactive decay is a process that follows a first-order rate law: Rate = kN

Question

1.     Radioactive decay is a process that follows a first-order rate law: Rate = kN, where N is the number of nuclei and the rate I the nuclear disintegrations per unit time. The half-life for the decay of 239Pu is 24,360 yr. The half-life for the decay of 241Pu is 13 yr.

a.     Calculate the rate constants for the decay of 239Pu and 241Pu.

b.     Which species decays more rapidly?

c.     If one starts with 5.0 g of pure 241Pu, how many disintegrations per second occur initially? What mass of 241Pu is left after 1.0 yr, 10 yr, 100 yr?     I find part c especially confusing??

Explanation / Answer

For radio active decay-

Rate constant = ln(2)/(half life) = 0.693/(halflife)

a. decay constant of Pu(239) = 0.693/(24360) per year

decay constant of Pu(241) = 0.693/(13) per year

b. ofcourse we can see Pu(241) decays to its half in just 13 years so it decays very rapidly as compared to the other one which takes 24360 years to decay to half of the initial amont

c. its very simple-

always stick to the formula- disintegration rate = timeconstant * number of nuclei at that moment

this further simplifies to - number of nuclei at a time t = initial number of nuclei * exp(-timeconstant * t)

so 5 gram of 241Pu contains 5/244 moles of Pu initially.

1 mole contains 6.023 * 10^23 atoms (Avogadro number) so 5/244 will contain (5/244)*6.023*10^23 atoms initially

So now you have initial number of atoms, time is given, time constant we have calculated in part A. all you have to do is put the values and evaluate the number of atoms at different 't' values (that is 1yr, 10yr and 100yr) . Hope i made it clear. :) please rate if you understood it :) thankyou

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.