Peoples Physics Book Version-2

http://www.ck12.org Chapter 27. Quantum Mechanics Version 2

a lower one. For example when an electron drops from− 3 .4 eV to− 13 .6 eV in the Hydrogen atom a 10.2 eV

photon is emitted. The spectra can be in infra-red, visible light, ultra-violet and evenX−rays. (The 10.2 eV

photon is ultra-violet.)

• The wave nature of electrons makes it impossible to determine exactly both its momentum and position. The
  product of the two uncertainties is on the order of Plank’s Constant. (Uncertainty in the electron’s energy and
  time are likewise related.)

The Key Equations

E=h f

Relates energy of a photon to its frequency.

p=

h

λ

Relates the momentum of a photon to its wavelength.

λ=

h

p

The Debroglie wavelength of an electron.

∆x∆p≥

h

4 π

This is the Heisenberg Uncertainty Principle, (HUP) which relates the uncertainty in the momentum and position of
a particle.

∆E∆t≥

h

4 π

Relates the uncertainty in measuring the energy of a particle and the time it takes to do the measurement.

h= 6. 626 × 10 −^34 J-sec

Planck’s constant.

1 eV= 1. 602 × 10 −^19 J

The most convenient unit of energy at the atomic scale is the electron volt, defined as the potential energy of the
charge of an electron across a potential difference of 1 volt.