In radioactive decay, λ₂=3λ₁. Initially the numbers of nuclei of A₁ and A₂ are equal. Find N₁/N₂ after one half-life of A₂.
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In radioactive decay, λ₂=3λ₁. Initially the numbers of nuclei of A₁ and A₂ are equal. Find N₁/N₂ after one half-life of A₂.

G1 Physics · Accepted Answer

At t=(ln2)/λ₂=(ln2)/(3λ₁), N₁/N₂= e ( λ 2 − λ 1 ) t e^{(λ₂-λ₁)t} e ( λ 2 ​ − λ 1 ​ ) t = e 2 λ 1 ⋅ l n 2 / ( 3 λ 1 ) e^{2λ₁·ln2/(3λ₁)} e 2 λ 1 ​ ⋅ l n 2/ ( 3 λ 1 ​ ) =2^(2/3).