Download Review for Chapter 7

Review for Chapter 7: Quantum Theory and the Electronic Structure of Atoms
1. Planck discovered that atoms and molecules emit energy only in certain quantities called “quanta”.
2. A quantum is the smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation.
3. Energy is always emitted or absorbed in whole-number multiples of h where h = 6.6256 x 10-34 J•sec (Planck’s constant)
and  is the frequency of the radiation in Hz (= 1/sec).
E = h
4. A wave is a vibrating disturbance by which energy is transmitted.
5. A wave is characterized by its wavelength (), its frequency (), and its amplitude.
The wavelength () is the distance between two identical points on successive waves.
The frequency () is the number of waves that pass through one point in 1 second.
The amplitude is the vertical distance from the maximum or minimum point of a wave to the midline.
6. The velocity of a wave, u, is the product of the wavelength and the frequency:
The velocity of an electromagnetic wave is equal to c, the speed of light:
where c = 3.00 x 108 m/sec
u = 
c = 
7. An electromagnetic wave has an electric field component and a magnetic field component, which have the same
wavelength and frequency but travel in perpendicular planes.
8. Electromagnetic waves occur over a broad spectrum of wavelengths (10 -3 to 1013 nm) and frequencies (1020 to 104 Hz).
This spectrum includes gamma rays, X-rays, ultraviolet rays, visible light waves, infrared waves, microwaves, and radio and
TV waves (see Figure 7.4).
9. Visible light ranges from a wavelength of approximately 400 nm (violet) to about 700 nm (red).
10. Einstein figured out how to explain the photoelectric effect, which is observed when electrons are ejected from the
surface of certain metals exposed to a light of a certain threshold frequency. He proposed that a beam of light is composed of
a stream of particles called photons. The photons have an energy E = h.
11. When energized with thermal energy or a high-voltage electrical discharge, substances emit a spectrum of radiation. The
emission spectra of atoms in the gas phase give a series of bright lines in different parts of the visible light range. Every
element has a unique and characteristic emission spectrum (see Figure 7.8). These line spectra can be used for the
compositional analysis of a sample.
12. Bohr provided a theoretical explanation of the emission spectra of hydrogen atoms. He showed that the energies, En,
that an electron in a hydrogen atom can possess are described by:
En = -RH (1/n2) where RH = 2.18 x 10-18J (the Rydberg constant) and n = the principal quantum number.
13. The change in energy resulting from the emission of a photon of frequency  and energy h for a hydrogen atom is
∆E =h = RH (1/ni2 – 1/nf2) where RH = 2.18 x 10-18J (the Rydberg constant), ni is the initial quantum number, and nf is the
final quantum number.
14. The Lyman, Balmer, Paschen, and Brackett series are sets of lines found in the emission spectrum of atomic hydrogen
and are explained by electron energy level transitions as shown in Figure 11. When an electron drops from a higher-energy
state to a lower-energy state, it emits a photon with a specific amount of energy.
15. The ground state is the lowest (most stable) energy state of a system. An excited state is a higher energy state of a
system that can be produced by putting radiant energy into an atom or molecule.
16. Electrons exhibit properties of both particles and waves.
17. DeBroglie proposed that if an electron behaves like a standing wave in a hydrogen atom, the length of the wave must fit
the circumference of the orbit exactly. This leads to 2r = n where r is the radius of the orbit,  is the wavelength of the
electron, and n is an integer (1, 2, 3, …).
18. DeBroglie related the particle and wave properties of a substance using  = h/mu where  is the wavelength of the
moving object, h = 6.6256 x 10-34 J•sec (Planck’s constant), m is the mass, and u is the velocity. Since Planck’s constant is
so small, wave properties are observable only for submicroscopic objects of very low mass.
19. Heisenberg’s uncertainty principle states that it is impossible to know simultaneously both the momentum p (defined
as mass x velocity) and the position, x, of a particle with certainty:
∆x∆p ≥ (h/4) where h = Planck’s constant
20. Schrödinger formulated an equation to describe the behavior and energies of electrons in terms of a wave function, .
An atomic orbital can be considered as the wave function of an electron in an atom.
21. The probability of finding an electron in a certain region in space is proportional to the square of the wave function,
2.
22. Schrödinger’s wave function uses four quantum numbers to describe the distribution of electrons in an atom:
f(n, l, ml, ms).
23. The principal quantum number, n, identifies the main energy level or shell of the orbital. It can have values of 1, 2, 3,
4, …
24. The angular momentum number, l, identifies the “shape” of the orbital. For a given value of the principal quantum
number, n, l can have values ranging from 0 to (n-1). The value of l is usually given as a letter: s for l = 0, p for l = 1, d for l
= 2, f for l = 3, g for l = 4, h for l = 5, etc.
25. The magnetic quantum number, ml, identifies the orientation of the orbital in space. The value of ml depends on the
angular momentum number, l, and can range from – l, (-l + 1), …, 0, … (+l -1), + l. The number of ml values represents the
number of orbitals in a subshell with a specified l value.
26. The electron spin quantum number, ms, identifies the direction of spin of an electron. It has a value of + ½ or - ½.
27. Atomic orbitals have different shapes: s orbitals are spherical, p orbitals have two lobes (one on each side of the
nucleus), d orbitals have four lobes or two lobes with a ring, and the shapes get more complicated for f and higher orbitals.
28. The energy of the electron in a hydrogen atom is determined solely by its principal quantum number, n.
29. No two electrons in an atom can have the same four quantum numbers (Pauli exclusion principle).
30. The most stable arrangement of electrons in a subshell is the one that has the greatest number of parallel spins
(Hund’s rule).
31. Atoms with one or more unpaired electron spins are paramagnetic and are attracted by a magnet. Atoms in which all of
the electron spins are paired are diamagnetic and are slightly repelled by a magnet.
32. The Aufbau principle provides guidelines for arranging (“building up”) the electrons in the atomic orbitals. The atomic
subshells are generally filled according to the following order:
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p
33. Only two electrons can be placed in each specific orbital. This gives the following totals for each type of orbital:
s orbitals: 2 electrons, p orbitals: 6 electrons, d orbitals: 10 electrons, f orbitals: 14 electrons.
34. Ground state electron configurations can be written by specifying each of the orbitals used and the number of
electrons placed in each orbital. For example, for calcium, Ca, which has 20 electrons: 1s 22s22p63s23p64s2. The electron
configuration can also be shortened by writing the nearest preceding noble gas structure in parentheses followed by the
required additional orbitals. For calcium, Ca: [Ar] 4s 2.
35. The periodic table is arranged according to how the subshells are filled (see Figure 7.28).