A sample of tritium-3 decayed to 94.5% of its original amount after a year. What is the half-life of tritium-3?

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Steven Arredondo · Accepted Answer

Step 1  A=A0e−kt  t is in years  After 1 year t=1 and A=0.945A0  Substitute to get  1) 0.945=e−k  Let half life be x. Then A=0.5A0  Substitute to get 0.5=e−kx  0.5=(e−k)x  Substitute 0.945−e−k Using eqn(1)  0.5=(0.945)x  Take ln⁡ on both sides to get  ln⁡(0.5)=xln⁡(0.945)  x=ln⁡(0.5)ln⁡(0.945)=12.25  Half life is 12.25 years

Elizabeth Witte · Accepted Answer

Step 1  Notice,  P(t)=P0ekt  Where, growth rate  k=−λ=−ln⁡2t12  Since, the amount after time t=1 year decays to P(t)=94.5% of initial value P0 hence substituting the corresponding values in the formula as follows  94.5100P0=P0e−λ×1  e−λ=0.945  λ=−ln⁡(0.945)  Hence the half life of tritium-3 is given  t12=ln⁡2−ln⁡(0.945)=12.25 years

A sample of tritium-3 decayed to 94.5\% of its original

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