WAEC Physics 2017 Theory — Question 33
Question 33 of 33 from the West African Examinations Council (WAEC) Physics 2017 Theory paper, with the correct answer and a full explanation.
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12(c) A piece of ancient bone from an excavation site showed 14C activity of 9.5 disintegrations per minute per 1.0x10^-3kg. If a bone specimen from a living creature shows 14C activity of 12.0 disintegrations per minute per 1.0x10^-3kg, determine the age of the ancient bone. [Half-life of 14C = 5572 years]
Model answer
T1/2=5572 years. Decay constant λ=0.693/T1/2=0.693/5572=1.244x10^-4 yr^-1. N0=12.0min^-1 per 1.0x10^-3kg (living); N=9.5min^-1 per 1.0x10^-3kg (ancient). N/N0=9.5/12.0=0.7917. Using N/N0=e^-λt: 0.7917=e^-λt. ln(0.7917)=-λt ⇒ -0.2336=-λt. t=0.2336/λ=0.2336/1.244x10^-4 = 1877.8 ≈ 1878 years.
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