Electronic Structure of Atoms
Quantum Theory
1. Atoms and molecules can only exist in certain states characterized by
definite amounts of energy. When an atom or molecule changes its state,
it absorbs or emits an amount of energy (electromagnetic radiation) just sufficient to bring it to another state.
Electronic energy
- ---form of energy that arises from the motion of e^{-} about the
nucleus, and from the interactions among the e^{-} and between the e^{-} and the nucleus.
- --only certain values of electronic energy are allowed for an atom
- --said to be quantized
- --a change of electronic energy level (state) of an atom involves the
absorption or emission of a definite amount, quantum, of energy
- --lowest electronic energy state is called the ground state
- --any state with energy greater than that of the ground state is an
excited state
2. When atoms or molecules absorb or emit light in moving from one energy state
to another, the wavelength of the light is related to the energies of the two states by the equation
E_{final} - E_{initial} = hc/l
h = Planck's constant
c = speed of light
- --ray of light can be considered to consist of photons
- --each photon of wavelength has an energy of hc/l
- --an atom or molecule can move from one electronic energy state to
another by absorbing or emitting a photon of energy
- --if it absorbs a photon of energy, hc/l , it moves from a lower
to a higher energy state, and its energy increases by hc/l
therefore: DE = E_{final} - E_{initial} = E_{hi} -E_{lo} = hc/l
3. The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers
- --quantum numbers are associated with individual electrons in an atom.
Relation between Energy difference, DE, and wavelength.
- --wavelength is inversely related to the energy difference, DE
a large DE---short wavelength........<400 nm--ultraviolet
a small DE---long wavelength.........>700 nm--infrared
- --e^{-} moves from one energy state to another by absorbing or emitting radiation of a particular wavelength.
- --by measuring the wavelength associated with e^{-} transition, we can find DE of the two energy states involved
h = 6.626 x 10^{-34} J . s/ particle
c = 2.998 x 10^{8} m/s
DE is in J/particle when wavelength is in meters
Ordinarily: DE is in kJ/mol, and wavelength is in nm
1 mole = 6.02 x 10^{23} particles
1 kJ = 10^{3} J
1 nm = 10^{-9} m
Relation between wavelength and frequency:
For example:
Blue light, at a wavelength of 450 nm, has a higher frequency than red light with a
wavelength of 650 nm.
- blue.....frequency = c/450 nm = 6.66 x 10^{14}/s
- red......frequency = c/650 nm = 4.61 x 10^{14}/s
- --DE is directly proportional to the frequency of the light absorbed or emitted
- --if DE is large, the light will have a high frequency
- --if DE is small, the light will have a low frequency
The Atomic Spectrum of Hydrogen and the Bohr Model
1911--Niels Bohr, Danish physicist
- -developed mathematical model for the behavior of an e^{-} in the hydrogen atom
- -based: on the Rutherford atom & quantum theory of Planck
spectroscope--instrument that breaks up light into its component colors
- --continuous--contains all the colors (such as in white light)
- --sodium vapor lamps, neon signs: the light given off looks different
-spectrum not continuous
-the light consists of several discrete colors which appear as lines of
definite wavelength when seen in a spectroscope
-each element has its own characteristic spectrum
Hydrogen most studied because it is the simplest with only 1 e^{-}
3 Points to keep in mind:
1. zero energy--the point at which the proton and e^{-} are completely separated
energy had to be absorbed to reach that point e^{-} in all its energy states within the atom must have energy below zero, i.e. must be negative
2. the normal H atom; the e^{-} is in the ground state when n = 1. When the e^{-} absorbs energy it moves to a higher excited state.
n = 2 (1st excited state), n = 3 (2nd excited state, etc.)
3. when an excited e^{-} gives off energy in the form of light, it drops back to a lower energy state
if e^{-} returns to ground state (n = 1): Lyman series (n = 2 to n = 1, n
3 to n = 1, etc.)
if e^{-} returns to the first excited state : Balmer
series ( n = 3, 4, ... to n = 2)
if e^{-} has a transition back to n = 3: Paschen series
Example
ionization energy of the H atom can be calculated from the Bohr model
H_{(g)} -------> H^{+}_{(g)} + e^{-}
DE = ionization energy
DE = 0 - (-1312 kJ/mol) = 1312 kJ.mol
Quantum Mechanical Atom
- --Bohr's model was great for the H atom (error of .1%); however,
even with He error increased to 5%
Wave Nature of the Electron:
- --deBroglie: suggested that particles might exhibit wave properties
wavelength = h/mv
m = mass
v = speed
2pr = nl
mvr = h n/2p
- --big question arises--how does one specify the position of a wave at a particular
instant?
- --can determine wavelength, energy, amplitude--but no way to tell just where the
electron is because a wave extends over space
- --Quantum mechanics was developed to describe the motion of small particles confined to very small portions of space.
- --deals with the probability of finding a particle within a given region of space
- --Schrodinger derived an equation from which one could calculate the amplitude (height) y of an electron wave at various points in space.
- --Several expressions for y that will satisfy the equation. Each is assoicated
with a set of quantum numbers.
- --Becomes possible to determine the probability of finding a particle in a given region
of space.
- --y^{2} proportional to the probability of finding the particle at that point
- --y^{2} proportional to the electron charge density at that point
Send comments or questions to:
Gwen Sibert
Roanoke Valley Governor's School
gsibert@rvgs.k12.va.us