At t = 0, the number of A nuclei is twice the number of B nuclei. Both have the same decay constant λ; A decays to B and B decays to a stable product. Which graph correctly represents the number of B nuclei versus time? Image
Options

Question

At t = 0, the number of A nuclei is twice the number of B nuclei. Both have the same decay constant λ; A decays to B and B decays to a stable product. Which graph correctly represents the number of B nuclei versus time? Image

Options

G1 Physics · Accepted Answer

Let N₁ be A nuclei and N₂ be B nuclei. Then dN₁/dt = −λN₁ and dN₂/dt = λN₁ − λN₂, with N₁(0) = 2N₂(0). Solving gives N₂(t)/N₂(0) = exp(−λt)(1 + 2λt). This initially rises and later falls, matching option C.