A hydrogen atom is modeled as an electron that can occupy only those circular orbits…
CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom
Problem
A hydrogen atom is modeled as an electron that can occupy only those circular orbits for which its wave-like nature "fits" around the orbit exactly.
Answer the following regarding the stability of these orbits and the resulting energy structure of the atom.
(a) Explain why an orbit whose circumference equals an integer multiple of the electron’s wavelength produces a stable standing‐wave state, whereas an orbit with a non-integer multiple does not.
(b) Describe qualitatively what would happen to an electron initially placed in a circular path whose circumference is not an integer multiple of its wavelength. Your answer should address the electron’s wave interference and the eventual fate of such a path.
(c) As the principal quantum number n increases from n=1 to large values, predict how the spacing between successive allowed energy levels changes. Justify your prediction using the standing-wave argument rather than any memorized energy formula.