Question

There are two radioactive elements, elements A and B. Element A decays into element B with a decay constant of 5łyr, and element B decays into the nonradioactive isotope of element C with a decay constant of 1lyr. An initial mass of 5 kg of element A is put into a nonradioactive container, with no other source of elements A, B, and C. How much of each of the three elements is in the container after tyr? (The decay constant is the constant of proportionality in the statement that the rate of loss of mass of the element at any time is proportional to the mass of the element at that time.) Write the equation for the mass, m(t), for each element based on time. ma(t)= m(t) = mc(t) =

Answer 1

dme 100-56 dt + me which is linear Equation, si dr I-F = ( e 4 e -56 E maet sices moet- 10 10 je Welt de 10 -46 e to - e-t tce -56 MR -se When t=0 =) mo = 0, -5tc. 2 CE wild -st 5 e -6 5 e mo E - un Mily Given non radio active cis the Growth rate does not Hence it decay rate of mo. of C is decay dmc = KMB so de Ek [-se Seftçet] Given K= dmc de 5e + 2 buth sides .56 ontegrating G 5 e سے tc = x I mc 56 1 me = s et to 11 ya

When LE then mac S 1 2.. -ute SC 353 l! 5 è