Chapter 5, Problem 28P

Quantum mechanics predicts that the energy of the ground state of the H atom is $-13.6eV$ . Insight into the magnitude of this quantity is gained by considering several methods by which it can be measured.

(a) Calculate the longest wavelength of light that will ionize H atoms in their ground state.

(b) Assume the atom is ionized by collision with an electron that transfers all its kinetic energy to the atom in the ionization process. Calculate the speed of the electron before the collision. Express your answer in meters per second $\left({\text{m s}}^{-\text{1}}\right)$ and miles per hour $\left({\text{miles h}}^{-\text{1}}\right)$ .

(c) Calculate the temperature required to ionize a H atom in its ground state by thermal excitation. (Hint: Recall the criterion for thermal excitation of an oscillator in Planck’s theory of blackbody radiation is that $hv\approx k_{B}T$ .)