Lecture 2210/26/05

Moving between energy levels

1. Hydrogen atom has only certain allowable energy levels 1. Stationary states 2. Atom does not radiate energy while in stationary state 3. Electron moves between stationary states by absorbing or emitting a photon of energy Good for 1 electron H atom, but failed to predict the spectrum for any other atom Bohr Model of the Hydrogen Atom (Recap)

de Broglie (1924) proposed that if light can have both wave and particle properties, then perhaps so could particles, such as electrons.

De broglie’s equation Equation is only useful for very small particles. For example, consider a 114-g baseball thrown at 110 mph. mv = 5.6 kg-m/s

Calculate the de Broglie wavelength of an electron (9.11 x kg) moving at a velocity of 5.0 x 10 6 m/s.

Quantum Mechanics or Wave Mechanics Theoretical approach to understanding atomic behavior

Heisenberg Uncertainty Principle For an electron, it is impossible to simultaneously determine: The exact position AND The exact energy

WAVE FUNCTIONS (  Schrödinger developed mathematical models of electron 1. Behavior of the electron in the atom is best described as a standing wave 1. Only certain wave functions are allowed 2. Each  is associated with an allowed E n 3. Energy of electron is quantized   2 is proportional to the probability of finding an e - at a given point 5. Each  corresponds to an Orbital 1. Region of space within which an electron is probably found 6. Quantum numbers are part of the mathematical solution (address of each electron)

(Principal Quantum Number) n n = 1, 2, 3 … infinity Designates the electron shell Value of n determines the energy of electron Remember the E n = -Rhc/n 2 Value of n also measures size of orbital Greater n  larger orbital size

(Angular Momentum Quantum Number) l l = 0, 1, 2, 3, ….n-1 Each l corresponds to a different subshell with a different shape Value of lSubshell label 0s 1p 2d 3f

(Magnetic Quantum Number) m l n = ±1, ± 2, ± 3,..., ±l Orientation of the orbital within the subshell All have the same energy

Schrödinger equation does not explain closely spaced lines in some spectra of elements Red line at 656 nm in Hydrogen spectrum is really a pair of lines: nm and nm Called doublets

Magnetic Field

Proven experimentally that electron has a spin. Two spin directions are given by m s m s = +1/2 and -1/2 Each orbital  no more than 2 electrons! 4th quantum number (m s ) electron spin quantum number

m l  orbital -l l  orientation Summary: Quantum numbers n  shell1, 2, 3, 4,...  size and energy l  subshell0, 1, 2,... n – 1  shape m s  electron spin+1/2 and -1/2  spin