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Number of nuclei remaining, N = 600 - 450 = 150 after time 't'.

1. N/N₀ = 150/600 = 1/4
2. N = N₀e^(-λt) → t = ln(N₀/N)/λ
3. t = (1/λ) ln(N₀/N)
4. t = (2.303/λ) log₁₀(N₀/N)

Correct answer: t = (2.303/λ) log₁₀(N₀/N)

Solution

The correct formula for calculating time in terms of decay constant (λ) and the ratio of initial to remaining nuclei is t = (2.303/λ) log₁₀(N₀/N). This is derived from the exponential decay law.

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