Transcript Atomic Spectra and Atomic Energy States

Atomic Spectra and
Atomic Energy States
Reminder: A.S. 13.1.5-13.1.7 due Monday 3/23/15
A.S. 13.1.8-13.1.13 due Tuesday 3/24/15
WebAssign Quantum #3 due Tuesday 3/24/15
Emission Spectra
 When a gas is heated to a high temperature, or
exposed to a large electric field
 Electrons in the atoms absorb the energy
 When the electrons fall back down to the
original electron energy the energy is
emitted as Electromagnetic radiation
 To the right: hydrogen gas, exposed to high
electrical potential
How do we see spectral lines?
 Direct light through a diffraction grating, or a prism
 Light at different wavelengths will diffract or refract different
amounts
 The wavelengths that combine to give us the color we see
emitted can be separated in this way
 Hydrogen, for example, is composed of 4 main wavelengths of
light:
Absorption Spectra
 Sometimes, we see spectra showing us which
wavelengths were absorbed by a sample of gas:
 Interestingly, the wavelengths of light ABSORBED by
the gas are the SAME as those EMITTED by the gas…
“Balmer Series”
 Curiously (at the time!), the spectral lines always
occurred at very specific (discrete) wavelengths
 In 1885, Johann Balmer determined that the spectral
lines for Hydrogen always followed this pattern:
1
1 1
=𝑅
− 2
𝜆
4 𝑛
(n  an integer value ≥ 3)
But he couldn’t explain WHY this worked!
Review: Planetary Model
 Rutherford came up with the planetary model of the
atom:
 There is a central, dense, positively charged nucleus
 Electrons occupy a large space outside the nucleus
 Electrons occupy “orbits”, much like planets orbit the
sun (our center of the solar system)
 WHY doesn’t this work?
Electron Energy Levels
 Combining the ideas of Balmer and Rutherford, Niels
Bohr made an attempt to “correct” the fundamental
flaw of the planetary model using the following
assumption:
 Electrons exist with discrete energy in each orbit
(energy level)
 In order to move between energy levels, a discrete
amount of energy must be absorbed by or released
from the electron
Bohr Model of the Atom
 Electrons exist at specific radii
from the nucleus—energy
levels
 Quantitatively, the energy of
the electron in that energy
level can be determined using
the following relationship:
13.6
𝐸=− 2
𝑛
Characteristics of Electron Energy Levels
 As n increases, the energy levels become closer together (unlike
the diagram on the previous slide)
 As n approaches infinity, the total energy of the electron
approaches 0
 As E approaches zero, the force keeping the electrons bound to
the nucleus decreases
 Ionization Energy: The energy that must be added to an electron
in order to release it from the atom
Ways of ionizing an atom:
 Significantly increasing the temperature
 Bombarding it with additional electrons (high velocity
collisions)
 Subjecting it to a very high electric potential
 Causing photons to fall on the atoms
Limitations to Bohr’s Model
 Describes the behavior of the electron in a Hydrogen
atom really well…however:
 Does NOT treat any atom with more than one electron
 Assumes circular orbits
 Cannot predict INTENSITIES of emitted light—only
wavelength
 Does not predict the division of energy levels (i.e. the p,
d, f orbitals all have subdivisions)
So…now what?
 Schrodinger Theory:
 Assumptions:
 Electrons in the atom can be described by wave
functions
 Wave functions fit boundary conditions in 3
dimensions, allowing for multiple “modes” that have a
discrete energy state
 Electron has an undefined position, but there is a
probability that the electron exists in a position
Electron Wavefunctions
 Wavefunction (ψ): a function of position and time
 Mathematically the probability that an electron will
be in a particular position at a particular time can be
determined by the square of the absolute value of the
wavefunction at that time.
 In other words, there are places where electrons are
most likely to be found…not just circular orbits!
Hydrogen electron probability
 For each energy
level for
Hydrogen, there is
a probability curve
describing how
likely it is that an
electron can exist
in that position.
Uncertainty Principle
 Fundamental idea: wave-particle duality
 Since particles sometimes act like waves, and waves
sometimes act like particles, there isn’t a perfect,
clean way to divide physical objects into one category
or the other.
 Misconception alert! This has nothing to do with
experimental uncertainties!
 It’s all about measuring things with an indefinite
precision (remember those distribution graphs we
just saw? )
Heisenberg’s Uncertainty Principle
 It is not possible to simultaneously measure both the
position and the momentum of a particle.
 The more sure we are about the position of a particle,
the less certain we are about its momentum, and viceversa.
ℎ
∆𝑥∆𝑝 ≥
4𝜋
Another variation…
 We can also describe the uncertainty principle in
terms of Energy and Time:
ℎ
∆𝐸∆𝑡 ≥
4𝜋