Chapter 2: The Quantum-Mechanical Model of the Atom

Question 1

Define quantum-mechanical model.

Answer 1

A model that explains the behavior of absolutely small particles such as electrons and photons.

Question 2

Define electromagnetic radiation.

Answer 2

A form of energy embodied in oscillating, perpendicular electric and magnetic fields.

Question 3

How can we characterize a wave?

Answer 3

By its amplitude, wavelength, and frequency

Question 4

Define amplitude.

Answer 4

The vertical height of a crest (or depth of a trough) of a wave; a measure of wave intensity.

Question 5

What does amplitude determine in light?

Answer 5

The light’s intensity or brightness - the greater the amplitude, the greater the intensity.

Question 6

Define wavelength.

Answer 6

The distance between adjacent crests of a wave (or any two analogous points).

Question 7

What does wavelength determine in light?

Answer 7

The light’s color

Question 8

Define frequency.

Answer 8

For waves, the number of cycles (or complete wavelengths) that pass through a stationary point in one second. Directly proportional to the speed at which the wave is traveling.

Question 9

Define hertz (Hz).

Answer 9

1 cycle/s; 1/s; s^-1

Question 10

Formula relationship between frequency and wavelength.

Answer 10

c = λ * ν

Question 11

What is the speed of light (c)?

Answer 11

c = 3.00 x 10^8 m/s

Question 12

Visible light from longest wavelength to shortest wavelength.

Answer 12

ROYGBIV

Question 13

Visible light from lowest frequency to highest frequency.

Answer 13

ROYGBIV

Question 14

Why do objects appear a certain color?

Answer 14

Objects reflect the colors in which they appear and absorb most other colors.

Question 15

Define electromagnetic spectrum.

Answer 15

The range of the wavelengths of all possible electromagnetic radiation.

Question 16

Electromagnetic spectrum from low energy to high energy.

Answer 16

Radio, Microwave, Infrared, Visible Light (ROYGBIV), Ultraviolent, X-ray, Gamma-ray

Question 17

Define interference.

Answer 17

The superposition of two or more waves overlapping in space, resulting in either an increase in amplitude (constructive interference) or a decrease in amplitude (destructive interference).

Question 18

Define constructive interference.

Answer 18

The interaction of waves from two sources that align with overlapping crests, resulting in a wave of greater amplitude.

Question 19

Define destructive interference.

Answer 19

The interaction of waves from two sources that are aligned so that the crest of one overlaps the trough of the other, resulting in cancellation.

Question 20

Define diffraction.

Answer 20

The phenomena by which a wave emerging from an aperture spreads out to form a new wave front.

Question 21

What happens when light passes through two slits separated by a distance comparable to the wavelength of the light?

Answer 21

The diffraction of light through the slits results in an interference pattern. Each slit acts as a new wave source, and the two new waves interfere with each other. The resulting pattern is a series of bright and dark lines. At the center, the two waves travel equal distances and interfere constructively. At the point where the difference in distance is one-half on one wavelength, the interference is destructive and a dark line appears. Constructive again at one whole wavelength away.

Question 22

Define photoelectric effect.

Answer 22

The observation that many metals emit electrons when light falls upon the metal.

Question 23

Define binding energy.

Answer 23

Energy with which an electron is bound to the metal.

Question 24

Define threshold frequency.

Answer 24

The frequency at which the energy of a photon exceeds the energy with which an electron is held to the metal, thus ejecting an electron from the metal.

Question 25

What did Albert Einstein propose for the explanation of the photoelectric effect?

Answer 25

Light energy must come in packets, with the amount of energy (E) in a light packet depending on its frequency. The emission of electrons from the metal depends on whether or not a single photon has sufficient energy to dislodge a single electron. For an electron bound to the metal with binding energy Φ, the threshold frequency is reached when the energy of the photon is equal to Φ.

Question 26

Formula Energy relationship to frequency.

Answer 26

E = h * ν

Question 27

Define Planck’s constant (h).

Answer 27

h = 6.626 x 10^-34 J*s

Question 28

Define photon.

Answer 28

(quantum) The smallest possible packet of electromagnetic radiation with an energy = h*v.

Question 29

Formula Energy relationship to wavelength.

Answer 29

E = (h*c) / λ

Question 30

Formula threshold frequency.

Answer 30

h * v = Φ

Question 31

Formula kinetic energy of ejected electron.

Answer 31

KE = (h * v) - Φ

Question 32

Define wave-particle duality of light.

Answer 32

Sometimes light appears to behave like a wave, at other times like a particle. The behavior we observe depends on the particular experiment.

Question 33

Define emission spectrum.

Answer 33

The range of wavelengths emitted by a particular element; used to identify the element.

Question 34

Why does the emission spectrum of an atom consist of discrete lines?

Answer 34

Because the stationary states exist only at specific, fixed energies. The energy of the photon emitted when an electron makes a transition from one stationary state to another is the energy difference between the two stationary states.

Question 35

Relationship between stationary states and energy.

Answer 35

Transitions between stationary states that are closer together produce light of lower energy than transitions between stationary states that are farther apart.

Question 36

Define absorption spectrum.

Answer 36

A plot of the absorption of light of a sample of matter as a function of wavelength.

Question 37

Define de Broglie relation.

Answer 37

The observation that the wavelength of a particle is inversely proportional to its momentum.

Question 38

Formula de Broglie relation.

Answer 38

λ = h / (m*v)

Question 39

Define complementary properties.

Answer 39

Properties that exclude one another; that is, the more you know about one, the less you know about the other. For example, the wave nature and particle nature of the electron are complementary.

Question 40

Define Heisenberg’s uncertainty principle.

Answer 40

The principle stating that due to the wave-particle duality, it is fundamentally impossible to precisely determine both the position and velocity of a particle at a given moment in time.

Question 41

Define deterministic.

Answer 41

A characteristic of the classical laws of motion, which imply that present circumstances determine future events.

Question 42

What is a probability distribution map for an electron?

Answer 42

It is a statistical map that shows where an electron is likely to be found under a given set of conditions.

Question 43

Define indeterminacy.

Answer 43

The principle stating that present circumstances do not necessarily determine future events in the quantum-mechanical realm.

Question 44

Define orbital.

Answer 44

A probability distribution map, based on the quantum-mechanical model of the atom, used to describe the likely position of an electron in an atom; also an allowed energy state for an electron.

Question 45

Define quantum number.

Answer 45

One of the four interrelated numbers that determine the shape and energy of orbitals, as specified by the solution of the Schrodinger equation.

Question 46

Define principal quantum number (n).

Answer 46

An integer that specifies the overall size and energy of an orbital; the higher the quantum number n, the greater the average distance between the electron and the nucleus and the higher its energy. (n = 1, 2, 3, …)

Question 47

Define angular momentum quantum number (l).

Answer 47

An integer that determines the shape of an orbital. (l = 0, 1, …, n-1)

Question 48

Define magnetic quantum number (m>l).

Answer 48

An integer that specifies the orientation of an orbital. (m>l = -l, …, 0, …, +l)

Question 49

What is the letter designation of an orbital according to l?

Answer 49

l=0 : s
l=1 : p
l=2 : d
l=3 : f
l=4 : g
l=5 : h

Question 50

Define spin quantum number (m>s).

Answer 50

Specifies the orientation of the spin of the electron. (m>s = -1/2, +1/2)

Question 51

Define electron spin.

Answer 51

A fundamental property of electrons; spin can have a value of +1/2 or -1/2.

Question 52

Value of spin up?

Answer 52

+1/2

Question 53

Value of spin down?

Answer 53

-1/2

Question 54

Define principal level (shell).

Answer 54

The group of orbitals with the same value of n.

Question 55

Define sublevel (subshell).

Answer 55

Those orbitals in the same principle level with the same value of n and l.

Question 56

Formula number of orbitals in any sublevel.

Answer 56

2l + 1

Question 57

Formula number of orbitals in a level.

Answer 57

n^2

Question 58

Shape of s orbital (l=0).

Answer 58

Spherical, nodes within the sphere at which the probability is 0

Question 59

Shape of p orbital (l=1).

Answer 59

Dumbbell, node located at the nucleus. The three p orbitals differ only in their orientation and are orthogonal to each other.

Question 60

Shape of d orbitals (l=2).

Answer 60

Four have a clover leaf, one has a dumbbell with a donut around the center.