How long will it take for a radioactive isotope with a decay constant of 0.15 (which means a half life of 4.6 days) to decay to 5% of its original value?

(At = A0e^-kt)

A 3 days

B 4.6 days

C 5 days

D 10.73 days

E 19.97 days

We know that N=No exp (-kt), where k is the decay constant, 5% of its original value means N = (5/100) No

so, for t=t', N = (5/100) No, (5/100) No=Noexp (-kt'), (5/100) = exp (-kt')

Ln (5/100) = Lnexp (-kt') = - kt', - 2.99 = - 0.15t', so t' = 19.93

so the answer is E 19.97 days