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Question
CBSEENPH12047898

The half-life of 198Au is 2.7 days. The average life is

  • 4 days

  • 3.4 days

  • 3.9 days

  • None of the above

Solution

C.

3.9 days

The half-life and the decay constant are related as

              t12ln 2λ = 0.693λ

⇒              λ = 0.693t 12         

                     = 0.6932.7 day

                     = 0.6932.7 × 24 × 3600 s

since 2.7 day = 2.7 × 24 hours × 3600s 

             λ = 0.0000029 s-1

             λ = 2.9 × 10-6 s-1

Now average life

             λ = 1λ = 3.9 days