The hydrogen atom can be modeled as a single electron bound to a nucleus containing…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential
Problem
The hydrogen atom can be modeled as a single electron bound to a nucleus containing one proton. In its ground state the electron is most likely to be found at an average distance of about 5.3×10⁻¹¹ m from the nucleus, whereas in the first excited state that distance increases to approximately 2.1×10⁻¹⁰ m.
Use this information to analyze how the electrostatic interaction between the nucleus and the electron changes when the electron is promoted from the ground state to the first excited state. Assume the values of fundamental physical constants are available on the reference sheet provided with the exam.
(a) Describe qualitatively how the magnitude of the attractive electrostatic force exerted on the electron changes as its average distance from the nucleus increases from 5.3×10⁻¹¹ m to 2.1×10⁻¹⁰ m.
(b) Calculate the factor by which the magnitude of that attractive force changes between the two states.
(c) Explain how the change in electrostatic force you obtained in part (b) relates to the difference in ionization energies for an electron in the ground state versus the first excited state of hydrogen.