Question

A 50.0g g sample of 16n decays to 12.5g in 14.4 seconds. What is its half life

Answer 1

T is amount after time t 
Ao is initial amount 
t is time 
HL is half life 

log (At) = log [ Ao x (1/2)^(t/HL) ] 
log (At) = log Ao + log (1/2)^(t/HL) 
log (At) = log Ao + (t/HL) x log (1/2) 

( log At - log Ao) / log (1/2) = t / HL 
log (At/Ao) / log (1/2) = t / HL 

HL = t / [( log (At / Ao)) / log (1/2) ] 

HL = 14.4 s / [ ( log (12.5 / 50) / log (1/2) ] 

HL = 14.4 s / 2 = 7.2 seconds