Question

Radioactivity lab using equation age=1/k ln(1+D/P)

k=decay constant; D= # of daughter atoms in sample (beans); P= # of parent atoms in sample (M&M's)

if you found a container with 20 M&M's and 50 pinto beans, how old would you estimate the sample to be

Answer 1

age=1/k ln(1+D/P)

This equation comes from the radioactive decay equation ,[A]=[A]o exp(-kt)

where [A]=# of beans after time t (unchnged or undecayed ones)=P ,[A]o= initial # of beans=D+P

this equation gives, ln [A]o/[A]=kt or t=1/K ln [A]o/[A],this is equation of the form y=mx+c withc=0,linear equation and m=slope=1/K

plot t verus ln [A]o/[A] with your data and the slope of the curve will be equal to 1/K=decay constant,once you obtain that value you can put it in the equation,

your data must contain info about time,

time                  # of atoms decayed                          # of atoms remaining

10s                               0                                                 70

20s

30s

age=1/k ln(1+D/P)=1/K ln(1+50 /20)=1/K*1.253