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Electrons in Atoms. I. Waves and Particles. A. A New Atomic Model. Rutherford model of the atom Dense positively charged nucleus Mostly empty space Did not explain where the electrons are located around the nucleus

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a a new atomic model
A. A New Atomic Model
  • Rutherford model of the atom
    • Dense positively charged nucleus
    • Mostly empty space
    • Did not explain where the electrons are located around the nucleus
    • Did not explain why negative electrons did not move to the p+ in the nucleus and collapse atoms
a a new atomic model1
A. A New Atomic Model
  • Prior to 1900 :
    • Electrons are particles (concentration of energy and other properties in space and time)
    • Light is waves (energy spread out over a larger region of space and time; an oscillation that moves outward from a source.
a a new atomic model2
A. A New Atomic Model
  • New atomic model emerged as a result of experimentation with absorption and emission of light by matter.
  • Studies revealed a relationship between light and an atom’s electrons.
  • Light was shown to exhibit both particle and wave-like behaviors.
  • Electrons were also shown to exhibit dual wave-particle nature.
b waves
B. Waves
  • Velocity (c) – Unit: m/s
  • Amplitude (A) - distance from the origin to the trough or crest. Unit will be length (m, …)
  • Wavelength () - length of one complete wave ; peak-to-peak distance. Unit: m, nm…
  • Frequency ( or f ) - # of waves that pass a point during a certain time period
    • hertz (Hz) = 1/s or s-1
b waves1






B. Waves

greater amplitude


b waves2
B. Waves
  • Frequency & wavelength are inversely proportional

c = 

c: speed of light (3.00  108 m/s)

: wavelength (m, nm, etc.)

: frequency (Hz)

b waves3


 = c

 = 3.00  108 m/s

2.73 x 1016 s-1

B. Waves
  • EX: Light near the middle of the ultraviolet region of the EM spectrum as a frequency of 2.73 x 1016 s-1. Calculate its wavelength.


 = 2.73 x 1016 s-1

 = ? c = 3.00  108 m/s

= 1.10 x 10-8 m

b waves4


 = c

 = 3.00  108 m/s

4.34  10-7 m

B. Waves
  • EX: Find the frequency of light with a wavelength of 434 nm.


 = ?

 = 434 nm = 4.34  10-7 m

c = 3.00  108 m/s

= 6.91  1014 Hz

c electromagnetic spectrum
C. Electromagnetic Spectrum
  • Electromagnetic radiation – a form of energy that exhibits wavelike behavior as it travels through space
  • Electromagnetic spectrum – all forms of electromagnetic radiation together
c em spectrum















C. EM Spectrum





c em spectrum1
C. EM Spectrum





c em spectrum2
C. EM Spectrum
  • Spectroscopy – branch of science that studies the interaction of light and atoms.
    • Spectrum – pattern of  or  when electromagnetic radiation is separated into its parts.
    • Spectroscope – instrument used to measure the wavelength of light.
c em spectrum3
C. EM Spectrum
  • Continuous spectra – use a diffraction grating to separate the wavelengths into the visible light spectrum. Shows all wavelengths in a given range.
    • Example :
      • visible light (400 nm – 700 nm)
c em spectrum4
C. EM Spectrum
  • Emission (bright line) spectra
    • Each line = different wavelength of light.
    • Lines represent energy emitted as e- fall from excited state to lower/ground state (from high energy levels to lower energy levels)
    • Usage – analyze substances for elements present. Each emits its own color. (Stars/astronomy)
c em spectrum6
C. EM Spectrum
  • Absorption (black line) spectra – shows the fraction of incident radiation absorbed by the material over a range of frequencies.
c em spectrum7
C. EM Spectrum
  • Ground state vs. excited state
    • Ground state – Electrons in the atom are in the lowest energy levels.
    • Excited state – Electrons in the atom are in higher energy levels. Electrons become “excited” when they gain enough energy to jump to a higher energy level in the atom.
      • Example: flames, spectral tubes
d waves vs particles
D. Waves vs Particles
  • Waves can bend around small obstacles.
  • Waves can fan out from pinholes.
  • Particles effuse (trickle out) from pinholes.
    • Ex. Balloon gradually deflates.
e particle behavior of light
E. Particle Behavior of Light
  • Max Planck (1900)
    • Observed - emission of light from hot objects
    • Concluded - energy is emitted in small, specific amounts (quanta = bundle of energy)
e particle behavior of light1

Classical Theory

Quantum Theory

E. Particle Behavior of Light
  • Planck (1900)


e particle behavior of light2
E. Particle Behavior of Light
  • Einstein (1905) – observed the photoelectric effect. Electromagnetic radiation strikes the surface of the metal, ejecting electrons from the metal, creating an electrical current.
e particle behavior of light3
E. Particle Behavior of Light
  • Einstein (1905)
    • Concluded - light has properties of both waves and particles

“wave-particle duality”

    • Light moves like a wave, but transfers energy like a stream of particles.
e particle behavior of light4
E. Particle Behavior of Light
  • Photon – bundle of energy given off as light. A particle of electromagnetic radiation having zero mass and carrying a quantum of energy.
  • Quantum - minimum amount of energy that can be lost or gained by an atom
e particle behavior of light5
E. Particle Behavior of Light
  • The energy of a quantum of energy is proportional to its frequency.

E: energy (J, joules)

h: Planck’s constant (6.6262  10-34 J·s)

: frequency (Hz)

E = h

e particle behavior of light6
E. Particle Behavior of Light
  • EX: Find the energy of a red photon with a frequency of 4.57  1014 Hz.


E = ?

 = 4.57  1014 Hz

h =6.6262  10-34 J·s


E = h

E = (6.6262  10-34 J·s) (4.57  1014 s-1)

E = 3.03  10-19 J