I have a physics question

Question

The half-life of radium-226 is 1,600 years and the half-life of carbon-14 is 5,730 years. Mathematically prove that the decay constant for radium-226 is larger than the decay constant for carbon-14.

Answer 1

From 2^(-t/τ) = e^-kt = N/N₀ you can derive that k = ln(2)/τ where k is the decay constant and τ = 1/2-life

That means k is inverse with τ.... k(Ra)/k(C-14) = τ(C-14)/τ(Ra) = 5730/1600

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