How can half-life be calculated?

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Answer 1 · 2015-11-01T05:50:02

If the decay is exponential, i.e. #x=x_{0}e^{-kt}#, then the half-life is given by #ln(2)/k#.

Let #tau# be the half-life. #tau# is the time taken for #x_0# to reach #x_0/2#

#x_0/2=x_{0}e^{-ktau}#

#1/2=e^{-ktau}#

#2=e^{ktau}#

#ln(2)=ktau#

#tau=ln(2)/k#