EXTENDING THIS TO HYDROGEN Results from solving the Shrodinger equation for the hydrogen atom Z is the atomic number m e is the mass of an electron e is the charge of an electron or proton h is Planks constant r is atomic radius is the permittivity of free space Agrees with experimental results Constants combined= Rydberg constant
RYDBERG EQUATION: DERIVATION IF THE ENERGY OF A GIVEN ENERGY LEVEL IS DEFINED AS E N =-R H (1/N 2 ). WE CAN FIND THE DIFFERENCE IN ENERGY SHELLS BY E NF -E NI 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. Change= Final - initial
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 Z 2. 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 (1.16). 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 E The Balmer series is the hydrogen emission series that is in the visible region what does this mean about n f ? (homework you could look up, on an exam I’d tell you). Please type your answer into your iclicker
EXTENDING TO OTHER ATOMS: 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? Reflecte d 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. http://www.infoplease.com/images/ESCI112LASERS003.gif Why can’t we see the laser light until it hits the wall?
TRANSITIONAL EXAMPLE PROBLEM If a bag of potato chips has 1000 calories and 100 chips, how many calories are there per chip? How did you did you do that? Now if a laser pulse has 1 J Total and 1000 Photons how many joules per photon? Make an Equation using these two questions relating total energy to energy of a photon.
EXAMPLE PROBLEM: A monochromatic beam of light with a total energy of 2.5J contains 8.56x10 -4 mols of photons. What is the wavelength of the beam?
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? Emission Spectra is unique to individual elements Spectra can be collected and matched to known emission spectra to determine the element present. Flame tests Hydrogen Emission Spectra Fe Emission Spectra Flame test
EMISSION SPECTRA: APPLICATIONS IN ASTRONOMY Spectra is collected Compared to known ions Temperatures known
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? chlorophyll absorbs red light and reflects green light eyes see reflected green light
TIME TO REGRESS TO OUR 5 YR OLD SELVES Why is the sky blue?