Radioactive elements decay at a constant rate per unit mass of the element. Show that such decays

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Radioactive elements decay at a constant rate per unit mass of the element. Show that such decays obey equations of the form

dm dt = -km

where k is the decay rate of the element and m is the mass of the element present. The half life of an element is the time taken for one-half of any given mass of the element to decay. Find the relationship between the decay constant k and the half life of an element.

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