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

Answer 1

The decay constant (λ) is directly proportional to the inverse of the half-life (t1/2), i.e., λ ∝ 1/t1/2. Thus, since the half-life of radium-226 is shorter than that of carbon-14, the decay constant for radium-226 must be larger than that of carbon-14.