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Two radioactive materials X₁ and X₂ have decay constants 5λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that of X₂ will be 1/e after a time

Asked in CBSE AIPMT 2008 · Decay law and half-life

• (1) λ
• (2) 1/(2λ)
• (3) 1/(4λ)
• (4) e/λ

Step-by-step solution

Why the other options are wrong

• (1) comes from quotes a decay constant where a time is wanted; λ has units of inverse time.
• (2) comes from would follow from an exponent of 2λ, but the difference of the decay constants is 5λ-λ=4λ.
• (4) comes from carries the e of 1/e into the answer; writing 1/e=e⁻¹ matches the base e, and equating the exponents fixes 4λ t=1.

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