atomic spectra and atomic energy states reminder: a.s. 13.1.5-13.1.7 due monday 3/23/15 a.s....
TRANSCRIPT
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 3/24/15WebAssign Quantum #3 due Tuesday
3/24/15
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
Emission Spectra
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:
How do we see spectral lines?
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…
Absorption Spectra
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:
(n an integer value ≥ 3)But he couldn’t explain WHY this worked!
“Balmer Series”
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?
Review: Planetary Model
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
Electron Energy Levels
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:
Bohr Model of the Atom
𝐸=−13.6
𝑛2
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
Characteristics of Electron Energy Levels
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
Ways of ionizing an atom:
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)
Limitations to Bohr’s Model
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
So…now what?
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!
Electron Wavefunctions
For each energy level for Hydrogen, there is a probability curve describing how likely it is that an electron can exist in that position.
Hydrogen electron probability
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? )
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 vice-versa.
Heisenberg’s Uncertainty Principle
∆ 𝑥 ∆𝑝≥h4 𝜋
We can also describe the uncertainty principle in terms of Energy and Time:
Another variation…
∆𝐸 ∆ 𝑡≥h4𝜋