PHYSICS name: 203 Hydrogen Ionization Energy Exercise Your text works out the ionization energy of a generic atom on page 204. The derivation is missing some important pieces and, to my mind, does not do a good job of developing the concept. Lets do an ionization energy problem with a bit more rigor. Specically, we will account for the electrons kinetic energy. A hydrogen atom consists of an electron in orbit around proton. The electrons orbital radius is called the Bohr Radius and has the value 0.53 1010 m. Ionization refers to the process of adding enough energy to the electron to completely remove it from the electrostatic potential well of the nucleus (proton, in this case). This is analogous to the escape speed problem we discussed a few days ago. There the question was, What speed should I give a rocket (electron) sitting at Earths radius (Bohr radius) away from the center of the Earth (nucleus of the atom) such that it has zero kinetic energy at r . 1. Energy in Initial State: Draw a diagram of the hydrogen electron in orbit around the nucleus. Identify all the energy terms that contribute to the total initial energy of the system, Ei .
Ei = 2. Energy in Final State: In the nal state, the electron is innitely far from the proton, and both particles are at rest. Write down the nal energy terms = here:
Ef 3. Energy Principle The Energy Principle says that any dierence in energy between the initial and nal energies is due to work performed on the system. This work W is this ionization energy - the energy we need to add to the electron to completely remove (ionize) it from the
atom: W = Ef Ei . From your work in (1) and (2) above, write down the terms in the ionization energy:
W = 4. What two terms are left to calculate? One of them should be the initial kinetic energy of the electron, Ke,i . The text neglects this term, but it is important and we can calculate it. Use Newtons 2nd law to calculate the velocity of the electron in its orbit around the proton:
ve = Finally, what is the kinetic energy of the ground-state hydrogen-electron?
Ke,i = 5. Initial Potential E...