HYDROGEN ATOM AND SPECTROSCOPY.
Energy Levels for the Hydrogen
atom.
Energy levels for the Hydrogen Atom
Equation for energy level
of a hydrogen atom
• Results from solving the Schrödinger
equation for the hydrogen atom
• Z is the atomic number
• me is the mass of an electron
• e is the charge of an electron or proton
• h is Planks constant
• r is atomic radius
• e0 is the permittivity of free space
• Agrees with experimental results
ENERGY LEVELS
• According to the Schrodinger equation the energy level of a hydrogen-like atom is given by the
equation below. Given that R is equal to 2.17x10-18J, find the energy level of the n=1 and n=2
levels? What is the difference between these energy levels?
RYDBERG EQUATION: DERIVATION
• IF THE ENERGY OF A GIVEN ENERGY LEVEL IS DEFINED AS EN=-RH(1/N2).
WE CAN FIND THE DIFFERENCE IN ENERGY SHELLS BY ENF-ENI
Change= Final-initial
Either of these are often shown
in text books. Use whichever
you prefer but be sure not to
mix them up. One has a
negative one does not.
EMISSION/ABSORPTION SPECTRA
RYDBERG EXAMPLE
• I’ll do:
• The energy levels of hydrogen-like one-electrons of atomic number Z differ from
those of hydrogen by a factor of Z2. Predict the wavelength of the transition from
n=2 to n=1 in He+. (1.17)
RYDBERG EXAMPLE
A violet line is observed at 434 nm in the spectrum of atomic hydrogen.
Determine the values of n for the beginning and ending energy levels of the
electron during the emission of energy that leads to this spectral line.
Hints:
We are observing a line, therefore is a photon being absorbed or emitted?
Based on the answer to the above: is the final higher or lower than the initial? What does that
mean about DE
The Balmer series is the hydrogen emission series that is in the visible region what does this
mean about nf? (homework you could look up, on an exam I’d tell you).
• If we have all one type of atom, and we excite all of them to a particular energy
level, what will be true of the emitted light?
A) The photons will all have the same wavelength
B) The photons have different wavelengths
C) No photons will be emitted
D) The photons will have different energies
E) I do not know
Reflected vs. Emitted
• Emitted light comes from a particular source.
• Examples?
• Reflected light “bounces” off other objects
• Examples?
• Each time we think about light think about which it belongs
too.
LASERS
• Light Amplification by Stimulated Emission of Radiation.
Why can’t we see the laser light until it hits the wall?
http://www.infoplease.com/images/ESCI112LASERS003.gif
WHAT DO WE USE EMISSION SPECTRA FOR?
Hydrogen Emission Spectra
Fe Emission Spectra
Given the above, and furthermore, that elements have specific emission spectra,
what could we use spectroscopy of elements for?
WHAT DO WE USE EMISSION SPECTRA FOR?
Hydrogen Emission Spectra
Fe Emission Spectra
• Emission Spectra is unique to individual elements
Flame test
• Spectra can be collected and matched to known
emission spectra to determine the element
present.
• Flame tests
EMISSION SPECTRA: APPLICATIONS IN
ASTRONOMY
•Spectra is collected
•Compared to known ions
•Temperatures known
SPECTROSCOPY
microscopyU
**don’t memorize this
GREEN FLUORESCENT PROTEIN (GFP)
Tsien
Anthony Chan, Emory University
Lets combine everything we know to think about some
things.
TIME TO REGRESS TO OUR 5 YR OLD SELVES
• Why is the grass
green?
THE GRASS IS GREEN BECAUSE…
What happens if you shine green light
on the plants?
What happens if you shine red light on
the plants?
TIME TO REGRESS TO OUR 5 YR OLD SELVES
• Why is the sky blue?
WHY IS THE SKY BLUE?
TIME TO REGRESS TO OUR 5 YR OLD SELVES
• Why is the Sun Yellow/Orange?
• (hint: is it really? Remember our black body
radiation talk)
scienceblogs.com
WHY IS THE SUN YELLOW/ORANGE
WHY IS THE SKY BLUE?