19
Quantum Theory and the Atom
p. 864
Atomic spectra and atomic energy states
12.1.7 Outline how atomic spectra can be observed.
12.1.8 Explain how atomic spectra provide evidence for the quantization of energy in atoms.
12.1.9 Outline the Bohr model of the hydrogen atom.
12.1.10 State the limitations of the Bohr model.
Bohr Atoms and Quantum Atoms
 explain quantitatively the Bohr atomic model as a synthesis of classical and quantum concepts
 explain the relationship among the energy levels in Bohr's model, the energy difference between levels, and the
energy of the emitted photons
 use the quantum-mechanical model to explain naturally luminous phenomena
19.1 The Bohr Atom
Atomic Theory before Bohr
John Dalton (1808)
Billiard-Ball Model
Atoms are the smallest particle of matter  invisible, indivisible & indestructible spheres
Atoms of each element are identicle to each other and unique from all other elements
JJ Thompson (1897)
discovered “Cathode Rays” from the cathode (−) plate to the anode (+) plate
The mass of the particles (electrons) were nearly 2000 times smaller than a hydrogen atom
 evidence that there are particles smaller than the smallest atom (H)
Ernest Rutherford (1895) discovered positively charged α particles and β rays emitted by uranium
The Geiger-Marsden Experiment
 High energy α particles were directed at extremely thin gold foil surrounded by a fluorescent screen
 Nearly all of the α particles went nearly straight through the gold foil – less than 10° deflection
 nearly all of the gold is empty space
 The gold had a positive charge but no change in mass after the α particle bombardment
 negative charges were removed from the gold by the α particles
 but no α particles were captured by the gold (no change in mass)
 Some of the α particles were deflected more than 90°
 the α particles must have been repelled by a positively charged mass (same charge as the α particle)
Rutherford
developed the Nuclear Model of the atom based on the experiment of Geiger & Marsden
Nucleus =  the positively charged centre of the atom  having almost no volume and  nearly all of the mass
Electrons = the negatively charged particles that circulate around the nucleus
The Bohr Model of the Atom (p.870)
Neils Bohr
tried to explain inconsistencies between classical mechanics and the results of black body radiation (Kirchhoff),
the photoelectric effect (Planck & Einstein) as well as the atomic theory of Rutherford.
studied the spectrum of light emitted by hydrogen
determined the mathematical relationship that would explain the bright line spectral pattern of hydrogen
built upon the research of Balmer (visible spectrum) and Rydberg (ultraviolet)
Bohr Postulates
(p.871)
1.
Circular Orbits
Electrons exist in circular orbits about the nucleus.
The centripetal force is an electrostatic attraction between the nucleus (+) and the electrons (−)
2.
Energy Levels
Electrons can only orbit on certain discrete energy levels.
The energy levels are quantized (limited to a discrete set of values)
3.
Electron Jumps
An electrons does not emit energy (light) when it stays in the same orbital (energy level)
An electron can “jump” up to a higher energy level (excited state) if it absorbs energy equal to the
difference in energy levels
An “excited” electron can “jump down” to a lower energy level by releasing photons of energy equal to
the difference in energy levels.
Bohr related the difference in the electron energy levels (ΔE) to the energy of the photons of light emitted (ħf)
| Ef – Ei | = ΔE = ħf
Bohr determined the radius of the ground state (lowest) energy level of hydrogen = Bohr radius
r1 = 0.0529 nm = 5.29×10−11 m
Bohr determined the energy levels of hydrogen using the relationship
En  
13 .6eV
n2
where n = the principal quantum number (any integer representing the nth energy level.
Spectral Series – LUV VIS PASCHEN
LUV
VIS
PASCHEN
Lyman series = Ultraviolet
Balmer series = Visible (ROYGBIV)
Paschen series = Infrared
Limitations of the Bohr Model
19.2
jump down to ground state (E1)
jump down to E2
jump down to E3
|En – E1|
|En – E2|
|En – E3|
highest ΔE
small ΔE
– the calculations are only valid for hydrogen spectra
− the principles apply to the energy levels and spectra of all atoms
The Quantum Mechanical Atom
The radius and energy of the quantized electron orbitals were explained by de Broglie and Schrödinger.
de Broglie applied his idea of matter waves to the orbitting electrons. He concluded that wave bahaviour of the electrons must
form a standing wave pattern, so the orbital circumference must have an integral (whole number) of de Broglie wavelengths.
see Figure 19.11 (p878)
Schrödinger (1926)
− used de Broglie’s wave model to create a quantum theory of the atom based on waves.
− developed the Schrödinger wave equation = the basic quantum mechanical equation
− related the probability of an electron being at a specific position at a specific time based on the wave
function, ψ
The wave function, ψ, relates the amplitude of the wave and wave speed to the allowed orbits and
energy levels of the electrons.
The wave-particle nature of matter means that it is impossible to know both the position and the momentum of an electron at the
same time.
Quantum Numbers
principal quantum number
n
orbital quantum number
ℓ
magnetic
quantum number
mℓ
spin quantum number
ms
Pauli Exclusion Principle
energy level of electron
orbital shape within the energy level)
orientation in an external magnetic field
electron acts as a spinning charge producing its own magnetic field
n = 1, 2, 3, . . .
ℓ  s, p, d, f
mℓ = +1 or 0 or −1
ms = + ½ or − ½
two electrons in the same atom can have the same four quantum numbers
This principle helps to explain the periodic table  s-block, p-block, d-block and f-block,
periods, and magnetic properties of some elements.\