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# Momentum and Collisions

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An atom of mass M is initially at rest, in its ground state. A moving (nonrelativistic) electron of mass me collides with the atom. The atom+electron system can exist in an excited state in which the electron is absorbed into the atom. The excited state has an extra, "internal," energy E relative to the atom's ground state.

1) Find the kinetic energy that the electron must have in order to excite the atom. Express your answer in terms of E,me and M.

2) We can use the result from Part A to study a process of interest in atomic physics: a collision of two atoms that causes one of the atoms to ionize (lose an electron). In this case, is the energy needed to ionize one of the atoms called the ionization energy? The most efficient way to ionize an atom in a collision with another atom is for the collision to be completely inelastic (atoms stick together after the collision). If the collision were perfectly elastic, then translational kinetic energy would be conserved, and there would be no energy left over for exciting the atom. If the collision were partially elastic, then some of the initial kinetic energy would be converted into internal energy, but not as much as in a perfectly inelastic collision. In practice, interatomic collisions are never perfectly inelastic, but analyzing this case can give a lower bound on the amount of kinetic energy needed for ionization.

Is it possible to ionize an atom of 133Cs , initially at rest, by a collision with an atom 16O of that has kinetic energy K. initial of 4.0 electron volts? The ionization energy of the cesium atom is 3.9 electron volts.

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

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An atom of mass M is initially at rest, in its ground state. A moving (nonrelativistic) electron of mass me collides with the atom. The atom+electron system can exist in an excited state in which the electron is absorbed into the atom. The excited state has an extra, "internal," energy E relative to the atom's ground state.

QUESTION 1:
Find the kinetic energy that the electron must have in order to excite the atom. Express your answer in terms of E, me and M.

Let the initial velocity of the atom be v and the velocity of atom+electron system be v1,
Since the momentum are conserved in the collision, so
M*0 + me *v=(M+me)*v1 -> v1= me *v/( M+me)

After collision the system excited state has an "internal," energy E ...

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