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
The decay constant is inversely proportional to the half-life, so a shorter half-life corresponds to a larger decay constant. Since the half-life of radium-226 is 1,600 years and the half-life of carbon-14 is 5,730 years, it follows that the decay constant for radium-226 is larger than the decay constant for carbon-14.
