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λA = 5λ and λB = λ At t = 0, (N0)A = (N0)B Given, NA/NB = (1/e)^2 According to radioactive decay, N/N0 = e^−λt ∴ NA/NB = e^−λAt/(N0)A/(N0)B = e^−λBt From (1) and (2), NA/NB = e^(−5λ−λ)t

1. NA/NB = e^(−5λ−λ)t
2. NA/NB = e^(−λt)
3. NA/NB = e^(−5λt)
4. None of the above

Correct answer: NA/NB = e^(−5λt)

Solution

The decay constant for A is 5λ, and for B is λ. Using the radioactive decay formula, the ratio NA/NB simplifies to e^(−5λt)/e^(−λt) = e^(−5λt).

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