Chapter 2: The Quantum-Mechanical Model of the Atom

Question 1

Define electromagnetic radiation in the context of what both an electric and magnetic field are.

Answer 1

An electric field is a region of space where an electrically charged particle experiences a force. A magnetic field is a region where a magnetic particle experiences a force. Electromagnetic radiation can be described as existing as a wave composed of oscillating, mutually perpendicular electric and magnetic fields propagating through space.

Question 2

What is the speed of light?

Answer 2

3.00 x 10^8 m/s

Question 3

Define amplitude and describe how it affects the characteristics of light.

Answer 3

Amplitude is the vertical height of a crest (or depth of a trough). The amplitude determines the light’s intensity or brightness. The greater the amplitude, the greater the intensity.

Question 4

Define wavelength and describe how it affects the characteristics of light.

Answer 4

The wavelength is the distance between adjacent crests. The wavelength of light determines its color.

Question 5

Define frequency and describe how it affects the characteristics of light.

Answer 5

Frequency is the number of cycles that pass through a stationary point in a given period of time. The frequency of a wave is directly proportional to the speed with which the wave is traveling. The frequency is inversely proportional to the wavelength.

Question 6

What characteristic of light is responsible for the way we perceive colors in objects?

Answer 6

The multiple wavelengths in white light, from red light (750 nm) to violet light (400 nm), are responsible for the way we perceive light.

Question 7

Rate the kind of electromagnetic radiation on the spectrum from lowest frequency to highest.

Answer 7

1. Radio waves
2. Microwaves
3. Infrared
4. Visible light
5. Ultraviolet
6. X-ray
7. Gamma ray

Question 8

Define gamma ray.

Answer 8

Gamma rays are the form of electromagnetic radiation with the highest energy, lowest wavelength, and highest frequency. They are produced by the sun, other stars, and certain atomic nuclei on Earth.

Question 9

What does in phase mean in reference to waves?

Answer 9

In phase means the crests of two waves line up, causing constructive interference.

Question 10

What does out of phase mean in relation to waves?

Answer 10

Out of phase means the crest of one wave overlaps with the trough from the other, causing the two waves to cancel by destructive interference.

Question 11

Define diffraction.

Answer 11

Diffraction occurs when a wave encounters an obstacle or slit that is comprable in size to its wavelength, causing it to bend and diffract around it.

Question 12

Describe the photoelectric effect.

Answer 12

When light is shined upon certain metals, they emit electrons. Before quantum theory, scientists believed this occurred because the amount of energy transferred to the metal exceeded the binding energy of the electron and the metal. However, scientists found that the results did not support that hypothesis. Instead, light does not eject electrons from a metal regardless of its intensity or its duration. They found that light is not just a wave; it is a packet of light with wave-particle duality nature.

Question 13

Why doesn’t low-frequency light eject electrons from metal?

Answer 13

No single photon in low-frequency light has enough energy to dislodge an electron. So, even if the intensity of the light is increased, the electron will not dislodge. However, if the frequency of light is increased, then any single photon with sufficient energy will dislodge the electron from the metal.

Question 14

Describe the equation for determining the kinetic energy of an electron dislodged from a metal.

Answer 14

The kinetic energy of this electron is equal to the energy of the photon minus the binding energy of the electron.

Question 15

Define atomic spectroscopy.

Answer 15

The study of the electromagnetic radiation absorbed and emitted by atoms.

Question 16

Define emission spectrum and describe what it can tell us about an element.

Answer 16

An emission spectrum is a series of bright lines that are emitted by a single element when light is shined upon its atoms. It can be used to identify the element; that is how scientists know which elements make up a star based on its light.

Question 17

How did classical physics try to explain the discrete lines of emission spectra?

Answer 17

According to classical physics, an atom should emit a continuous white light spectrum and lose energy as it emits the light and spiral into the nucleus. An atom would not even be stable in the classical model. The new model however, could explain the lack of continuation in the emission spectra.

Question 18

Describe the Bohr model of the atom.

Answer 18

The Bohr model of the atom says that the electron orbits exist only at specific, fixed distances from the nucleus. When an electron jumps from one stationary state to another radiation is emitted or absorbed.

Question 19

Define flame tests and describe how they are used.

Answer 19

When put into a flame, elements cause the flame to become a distinct color. The presence of intense lines in the spectra of a number of metals is the basis for flame tests.

Question 20

Define absorption spectrum and describe how it is used.

Answer 20

Absorption spectrum works in the same way as emission spectrum. It is measured by passing white light through a sample and observing what wavelengths are missing due to absorption by the sample.

Question 21

What does the amount of light absorbed by a sample depend upon?

Answer 21

It depends upon the concentration of the absorbing sample.

Question 22

When electrons pass through two slits, how does interference happen?

Answer 22

While one might think interference occurs as a result of electrons interfering with each other, it is actually a result of electrons interfering with themselves. Light has a wave-particle duality, and so do electrons. Therefore, electrons can pass through both slits because it exists in both states. This principle is also what keeps the electrons in an atom from crashing into the nucleus.

Question 23

What are complementary properties?

Answer 23

Complementary properties are properties that exclude one another–the more you know about one, the less you know about the other. An example is the dual wave particle nature of electrons. If you observe one, you cannot observe the other.

Question 24

Explain Heisenberg’s uncertainty principle.

Answer 24

This principle essentially says that the more accurately you know the position of an electron, the less accurately you can know its velocity. The complementarity of the wave nature and particle nature of the electron results in the complementarity of velocity and position.

Question 25

Define probability distribution maps.

Answer 25

These maps give us a picture of where a quantum-mechanical particle is most likely to be found. Because the motion of these particles is not deterministic, there is no way to predict its trajectory; we can only guess where it is most likely to be.

Question 26

What are the four quantum numbers?

Answer 26

1. n, the principal quantum number.
2. l, the angular momentum quantum number
3. ml, the magnetic quantum number.
4. ms, the spin quantum number.

Question 27

What does the l orbital determine?

Answer 27

The angular momentum quantum number determines the shape. l = 0 corresponds to s orbitals; l = 1 corresponds to p orbitals, and l = 2 corresponds to d orbitals.

Question 28

Define probability density.

Answer 28

Probability density refers to the probability (per unit volume) of finding the electron at a point in space.

Question 29

Define radial distribution function.

Answer 29

The radial distribution function represents the total probability of finding the electron within a thin spherical shell at a distance r from the nucleus. It is equal to the probability density x volume of shell at r.

Question 30

At r = 0 (at the nucleus), describe where the probability density and radial distribution function are.

Answer 30

At r = 0, the probability density is at a maximum, however, the volume of a thin spherical shell is zero, so the radial distribution function is zero. As r increases the volume of the thin spherical shell increases.

Question 31

Define node.

Answer 31

A node is a point at which the wave function, the probability density, and the radial distribution function all go through zero.

Question 32

Define phase.

Answer 32

Phase refers to the sign of the amplitude of a wave–positive or negative.

Question 33

Explain how blackbody radiation overturned classical physics’ ideas of matter and light.

Answer 33

When objects are heated, they give off electromagnetic radiation. Classical physics says that blackbody radiation is a result of oscillators being thermally excited, and the resulting emission spectrum can be predicted by Rayleigh-Jeans Law. However, observation found that the EM spectrum given off by a blackbody shifts its maximum to lower wavelengths with increasing temperature. Spectral intensity drops to zero at very short wavelengths. Therefore, Rayleigh-Jean’s Law fails at high frequencies; if it were accurate, it would predict an infinite amount of ultra-short wavelength light emitted from a blackbody, but this is not the case.

Question 34

How did Planck resolve the blackbody problem?

Answer 34

He introduced three new physical concepts:
1. The energy of a blackbody must be discrete and quantized.
2. The system must gain or lose energy in discrete increments.
3. To excite higher energy states, temperature of the system must be sufficiently high.

Question 35

What does the magnetic quantum number describe?

Answer 35

The spatial orientation of the orbital.

Question 36

How many degenerate orbitals (energetically equivalent) are in a subshell?

Answer 36

2l + 1

Question 37

How are orbitals with the same value of n and l related?

Answer 37

They are said to be in the same subshell.

Question 38

How many angular nodes do d orbitals have?

Answer 38

Two angular nodes.

Question 39

How many angular nodes do f orbitals have?

Answer 39

Three angular nodes.

Question 40

How do you calculate the number of radial nodes of an orbital?

Answer 40

Number of radial nodes = n - l -1

Question 41

How do you calculate the number of angular nodes of an orbital?

Answer 41

The number of angular nodes = l

Question 42

How do you calculate the total number of nodes of an orbital?

Answer 42

Total nodes = n - 1

Question 43

How many orbitals are in a given n?

Answer 43

A given n contains n^2 orbitals.

Question 44

How many electrons are in a given n?

Answer 44

2n^2 electrons.

Question 45

How many orbitals are contained in each subshell?

Answer 45

Each subshell contains 2l + 1 orbitals.

Question 46

If the change in energy calculated by Rydberg’s equation is positive, was a photon absorbed or emitted?

Answer 46

If deltaE is positive, a photon is absorbed. If it were negative, a photon was emitted.