Answer to Question #347541 in Physics for Loie

Question #347541

How long would it take 4.0 x 10²⁰ atoms to decay to 1.0 x 10¹⁹ atoms if their half-life was 14.7 years?

1
Expert's answer
2022-06-06T08:55:16-0400
N=N02t/t1/2N=N_02^{-t/t_{1/2}}1.01019=4.010202t/14.7yrs1.0*10^{19}=4.0*10^{20}*2^{-t/14.7\:\rm yrs}t=14.7log2(1.01019/4.01020)=78yrst=-14.7*\log_2(1.0*10^{19}/4.0*10^{20})=78\:\rm yrs

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