Two radioactive materials A₁ and A₂ have decay constants 10λ₀ and λ₀. Initially they contain equal numbers of nuclei. After what time will the ratio of their undecayed nuclei be 1/e?
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Two radioactive materials A₁ and A₂ have decay constants 10λ₀ and λ₀. Initially they contain equal numbers of nuclei. After what time will the ratio of their undecayed nuclei be 1/e?

G1 Physics · Accepted Answer

N₁/N₂ = exp[−(10λ₀−λ₀)t] = exp(−9λ₀t). Setting this equal to 1/e gives 9λ₀t=1, so t=1/(9λ₀). Correct answer: B.