You can take the mass of the oxygen atom to be 16 atomic massunits and that of t

Question

You can take the mass of the oxygen atom to be 16 atomic massunits and that of the cesium atom to be 133 atomic mass units. Itdoesn't matter what mass units you choose, as long as you areconsistent. For this question, it is most convenient to use atomicmass units, since these are the numbers you are provided with.

Explanation / Answer

Since the collision would be perfectly inelastic, (M+me)*v = me*u => v = me*u/(M+me) => Ground state energy + me*u*u/2 = Ground state energy + E +(M+me)*v*v/2 => E = me*(u*u/2 - v*v/2) - M*v*v/2 = u*u/2 * [ me -(me+M)*(me/(M+me)^2) ] => E = me*u*u/2 * [ 1 - m/(M+me)] =K.E.*[M/(M+me)] => KE = E(M+me)/M In the inelastic collision the kinetic energy of the oxygen atomwould be used up partly as the ionization energy of cesium atom andpartly as kinetic energy of the combined entity. So, K.E.oxygen = I.E.cesium + K.E.(oxygen+cesium)    Mo*U = (Mo+Mcs)*V1 assuming least energy is required causing electron to bejust emitted. (2KMo) = (Mo+Mcs)*V1    => K' = P*P/2(Mo+Mcs) = KMo/(Mo+Mcs)    => K-K' = IE => K*[1 - Mo/(Mo+Mcs)] =Mcs*K/(Mo+Mcs)    => K = IE * (Mo+Mcs)/Mcs = IE * 149/133 = 3.9 *149/133 eV = 4.369 eV ~ 4.4 eV

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