8 | The Quantum Mechanical Atom 305
8.1 Electromagnetic Radiation 306
8.3 The Bohr Theory 316
8.5 Quantum Numbers of Electrons in Atoms 324
8.7 Energy Levels & Ground State Electron Configurations 328\
8.9 Atomic Orbitals: Shapes and Orientations 337
E = m c2
En = -b/n2
Eeach photon = h 
 = c
E = -b[
8.2 Line Spectra and the Rydberg Equation 314
8.4 The Wave Mechanical Model 318
8.6 Electron Spin 326
8.8 Periodic Table & Electron Configurations 330
8.10 Periodic Table and Properties of the Elements 340
h / (m v)
(1/nf2)
-
(1/ni2)
c = 2.998x 108 m/sec
b = 2.18x10-18 J
]
1/= b/hc [ (1/nf2) - (1/ni2) ] = RH [ (1/nf2) - (1/ni2) ]
h = 6.626x10-34 Jsec
J = kg m2 / sec2
RH = b/hc = 1.09678x107 /m
1. An argon ion laser emits light at 457.9 nm. What is the frequency of this radiation?
2. If the de Broglie wavelength of an electron is 15 nm, what is its velocity? The mass of an electron is 9.1  10-31 kg.
3. What is the energy (in kJ) of each photon of light with a wavelength of 450. nm? 1 mole of photons?
4. What is the energy associated with n=6? n=2?
6. What is the energy associated with a quantum leaping from n=6 to n=2? Per mole of photons?
7. Compare the answer to (6) with the energy associated with a quantum leaping from n=6 to n=1.
8. What is the wavelength associated with a quantum leaping from n=6 to n=2?
9. Compare the answer to (8) with the wavelength associated with a quantum leaping from n=6 to n=1.
10. Heisenberg uncertainty principle states that we cannot know exactly the position and velocity of an electron both at
the same instant. Explain what we studied under ‘position’ and under ‘velocity’. What were the assumptions when
studying ‘position’? “velocity”?
“Lyman series” if final n=1, “Balmer series” if final n=2, “Paschen series” if final n=3
Quantum numbers :
1) n = principal quantum number. – shell - size, energy, how many subshell types.. 1, 2, 3, 4, 5, 6..
2) l = angular momentum (secondary) quantum number - subshells(s, p, d, f, g, h…) -energy, shape,
number of nodal planes… 0, 1, 2, 3, 4, 5……to (n-1).
3) ml = magnetic quantum number - orbitals - describes the spatial orientation of the orbital. (how
many ‘boxes’ to draw) range from –l to +l
4) ms = spin quantum number - electrons +1/2 (up arrow) for the first one, -1/2 (down arrow)for the
second one.
n
l
ml
ms
Note
Trends In Atomic and Ionic Radii (pm)
7.8 Atomic properties correlate with an atom’s electron configuration
65