PHYS 2004 Lecture Notes - Lecture 31: Standing Wave

52 views1 pages

ultramarinemammoth89

1 Dec 2017

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

The orbital energy en of an electron in an atom is always negative. |en| is called the binding energy of an electron in stationary state n. Removing an electron from an atom leaves behind a positive ion. Since nearly all atoms are in their ground state, |e1| is called the ionization energy. The angular momentum of a particle in circular motion, whether it is a planet or an electron, is l. Since v and r can only have certain values for an electron standing wave, the angular momentum is also quantized:

Related Questions

An electron of momentum p is at a distance r from a stationary proton. The electron has kinetic energy . The atoms has potential energy and total energy . If the electron is bound to the proton to form a hydrogen atom, its average position is at the proton but the uncertainty in its position is approximately equal to the radius r of its orbit. The electron's average vector momentum is zero, but its average squared momentum is approximately equal to the squared uncertainty in its momentum as given by the uncertainty principle. Treating the atom as a one-dimensional system: (a) estimate the uncertainty in the electron's momentum in terms of r. Estimate the electron's (b) kinetic energy and (c) total energy in terms of r. The actual value of r is the one that minimizes the total energy, resulting in a stable atom. Find (d) that value of r and (e) the resulting total energy. (f) State how your answers compare with the predictions of the Bohr theory.