Electromagnetic spectrum
Characteristics of waves. Define each:
Frequency (υ) ____________________________________________________________________________________________________
Period (T) ______________________________________________________________________________
Wavelength (λ) ___________________________________________________________________________________________________
speed (v) c __________________________________________________________________________________
Amplitude (Intensity):___________________________________________________________________________________________
Mathematical relationships
T
υ
E
Know each section of the spectrum
R
LIGHT AS A WAVE:
Diffraction pattern
Refraction:
Reflection:
Interference:
O
Y
G
B
I
V
LIGHT AS A PARTICLE?
Photo electric effect: Max Planck and others observed that electrons are emitted from metal surfaces when
light strikes it. What were the observations?
1. Threshold frequency: ______________________________________________________________________
2. Intensity independence: ____________________________________________________________________
3. Number of electrons and intensity above threshold frequency: ____________________________________________
___________________________________________________________
4. Energy of electrons and intensity: _________________________________________________________________________
Why is this inconsistent with wave nature?
Einstein’s explanation
It takes 208.4kJ to remove the electrons from a mole of rubidium atoms. What is the wavelength of light that
would release an electron from that atom?
E =(208.4kJ/mole)* 1000J/kJ *(1mole/6.022 x 1023 electrons) = 3.462 x 10 -19 J/e
E = hυ υ = E/h = (3.462 x 10 -19 J/e)/6.626 x 10-34 = 5.225 x 1014 Hz
λ= c/υ = 2.998 x 108/(5.225 x 1014 Hz) = 5.738 x 10-7m = 537nm
Determine the energy of an electron emitted by a rubidium atom that is exposed to a 525nm beam of light?
If the energy is all kinetic energy (me = 9.11 x 10-31kg), what is the speed of the electron?
E=hc/λ = 6.626 x 10-34 Js* 2.998 x 108m/s/ (525 x 10-9m) = 3.784 x 10-19J
Eelectron = Ephoton – ionization energy=3.784 x 10-19J - 3.462 x 10 -19 J/e = 3.217 x 10-20 J =KE = ½ mv2
3.217 x 10-20 J = ½ 9.11 x 10-31kg * v2  v= 2.66 x 105m/s
DeBroglie’s hypothesis
E= hc/λ & E=mc2 Replace c (the speed of light) with v (the speed of any piece of matter) and set equations
equal to each other. hv/λ = mv2…solve for λ = h/mv or λ = h/p. Where p is momentum. So all matter has a
wavelength equal to Planck’s constant divide by the momentum of the particle. For macroscopic particles
(e.g. footballs, cars, people…) the wavelength is less than the thickness of an atom. Now determine the
wavelength of the electron in the previous problem.
λ = h/mv =6.626 x 10-34/(9.11 x 10-31kg * 2.66 x 105m/s) = 2.73 x 10-9 m (Atoms are on the order of
angstroms (10-10m across) So this leads to a wavelength that is bigger than an atom.
Davisson & Germer
Tested the wave particle duality measuring the wavelength of an electron and found close agreement with
DeBroglie’s equation.
Wave Particle Duality
Light can act like a wave and a particle, so can electrons. In the continuum between energy and matter
stated in Einstein’s famous equation, the electrons and photons are on the edge and can exhibit both
behaviors.
Bohr Atom: Planetary view of the atom.
Postulates
1. Energy level postulate: electrons can exist in only certain allowed orvitals. n=1,2,3,4…..
2. Transitions between energy levels: Electrons can jump between orbitals by gaining or losing energy
that is equivalent to the differences between those energy levels.
A. Absorption spectrum: When the entire spectrum is shined on an atom there will be missing bands of
electromagnetic radiation. Each of those bands corresponds to the difference between the energy
levels.
B. Emission spectra: After the electrons have been excited up to some higher levels, if left alone they will
drop back down to the lower levels. In doing so they will release E.M radiation that is identical to the
radiation that was missing in the absorption spectra.
3. Electrons do not radiate: As they rotate about the nucleus electrons do not lose energy.
Bohr’s equation: En = -RH/n2 ΔE = Ehi - Elo
Determine the wavelength of light associated with each of the following transitions in a hydrogen atom.
n=3 n=2
λ = 656nm
n=4 n=1
λ = 97.2nm