Question

How many nuclei of 238 92 U 92 238 U remain in a rock if the activity registers 290 decays per second?(Note that the half life of Uranium-238 is 4.468x109 years)

Answer 1

Use the activity formula,

T1/2 = 4.468 x 10^9 yr x 365 x 24 x 3600 = 1.409 x 10^17 sec

l = ln(2)/T1/2 = ln(2)/1.409 x 10^17 = 4.91932697 x 10^-18 s-1

DN/Dt = lN, 265 = 4.91932697 x 10^-18 x N

N = 5.38 x 10^19 nuclei