Lecture 22 10/26/05
Dec 21, 2015
s/m10998.2light of speed c
sJ1062.6constant sPlanck'h
m100974.1constant RydbergR
2n and 1n
n
1
n
1Rhc
n
Rhc
n
RhcEEE
8
34
7
2initial
2final
2initial
2final
initialfinal
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 state3. 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.
mv
hλ
λ
hmv
light) of c(speed for particle) of v(velocity subsitute particle, a For
λ
hmc
λ
hcmc
mcE and λ
hcE :light For
2
2
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
)range m10 the in are rays (gamma measure to smallinsanely Too
m 102.1λ
smkg 6.5
smkg 10626.6λ
mv
hλ
16
34
234
nm 15.0m 1
nm 10m 105.1λ
)s/m 100.5)(kg 1011.9(
smkg 10626.6λ
mv
hλ
910
631
234
Calculate the de Broglie wavelength of an electron (9.11 x 10-31 kg) moving at a velocity of 5.0 x 106 m/s.
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 En
3. Energy of electron is quantized4. 2 is proportional to the probability of finding an e- at
a given point5. 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 En = -Rhc/n2
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 l Subshell label
0 s
1 p
2 d
3 f
(Magnetic Quantum Number) ml
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: 656.272 nm and 656.285 nm
Called doublets
Proven experimentally that electron has a spin. Two spin directions are given by ms
ms = +1/2 and -1/2 Each orbital no more than 2 electrons!
4th quantum number (ms) electron spin quantum number