Question

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. Initial: Final: M Me 1 Part A Find the kinetic energy Ke that the electron must have in order to excite the atom. Express your answer in terms of E, me, and M. 1 Part C What is the least possible initial kinetic energy Kmin the oxygen atom could have and still excite the cesium atom? Express your answer in electron volts, to one decimal place.

Answer 1

To excite the atom, the electron must have enough kinetic energy to overcome the energy difference between the ground state and the excited state. The minimum initial kinetic energy that the oxygen atom could have and still excite the cesium atom is E/16.

Step-by-step explanation:

Part A: To excite the atom, the electron must have enough kinetic energy to overcome the energy difference between the ground state and the excited state, which is E. We can relate the kinetic energy of the electron to the initial potential energy it had before the collision. The electron's kinetic energy before the collision can be calculated as KE = eAV, where AV is the potential difference across which the electron was accelerated. Since the electron was initially at rest, AV can be equated to the initial potential energy of the electron. Therefore, KE = eAV = E.

Part C: The minimum initial kinetic energy (Kmin) that the oxygen atom could have and still excite the cesium atom can be calculated by equating the initial potential energy of the oxygen atom (Kmin) to the energy required to excite the cesium atom (E). So, Kmin = E. Since the rest-mass energy of the oxygen atom is approximately 16 times that of the electron, we can express Kmin in electron volts (eV) as Kmin = E/16.