Radium-221 has a half-life of 30 sec. How long will it take for 76% of a sample to decay?

Question

Radium-221 has a half-life of 30 sec. How long will it take for 76% of a sample to decay?

Answer 1

A = A₀e^rt; If t = 30 s then A = A₀/2; A₀/2 = A₀e^30r; e^30r = 1/2; r = ln(1/2)/30 = - 0.0231;A = A₀e^{- 0.0231t};

A = 0.24A₀; 0.24 = e^{- 0.0231t}; t = - ln0.24/0.0231 = 61.78 s