Quantum Theory and Atomic structures

Question 1

The Wave and Particle Nature of Light
Limitations of the Planetary Model (Rutherford)
Two significant shortcomings:
1. Unlike planets orbiting a sun, electrons are charged particles. An *electric charge is known to *. An orbiting charge should steadily * energy and * toward the nucleus, colliding with it in a small fraction of a second.
2. The planetary model could not explain the * and
* that were observed.

Answer 1

accelerating, emit electromagnetic waves
lose, spiral

highly peaked emission, absorption spectra of atoms

Question 2

• is a form of energy propagated as mutually * . It includes visible light, infrared,
  ultraviolet, X ray, and radio waves.

Answer 2

Electromagnetic radiation

perpendicular electric and magnetic fields

Question 3

A * is a disturbance that transmits energy through a medium.

Answer 3

wave

Question 4

• is the height of the crest of a wave above the center line of the wave.

Answer 4

Amplitude

Question 5

The * is the distance between successive crests or troughs of a wave motion. Designated by lambda.

Answer 5

wavelength

Question 6

The frequency of a wave motion is the * or troughs that

* through a given * in a unit of * . It is expressed by the unit time−1 (e.g., s−1, also called a hertz, Hz).

Answer 6

number of wave crests, pass, point, time

Question 7

distinctive feature of electromagnetic radiation is its constant * of in a
vacuum, often referred to as the speed of light.

Answer 7

speed c = frequency × wavelength

Question 8

In phase - *

Out of phase - *

Answer 8

Constructive Interference

Destructive Interference

Question 9

Blackbody Radiation and Classical Physics
A * is one that absorbs and emits all frequencies.
• As temperature T increases, the * of emitted light also increases.
• Spectral distribution of the intensity of blackbody radiation as a function of * . Increase in temperature shifts the maximum to * frequencies.
• Classical physics was unable to explain the distribution of frequencies.

Answer 9

blackbody
frequency
frequency
higher

Question 10

The first person to offer a successful explanation of blackbody radiation was *.
• He assumed that the * emitted by the body was due to the * of the electrons in the constituent particles in the material body. Similar to classical
physics.
* He then assumed that the * of the oscillators were proportional to an * of the *

Answer 10

Max Planck (1900)
radiation, oscillations 

energies
integral multiple n, frequency

Question 11

Planck’s law:

Answer 11

E = nhv

h - 6.626 * 10^-34 J-s

Question 12

In 1888,* discovered that * light caused electrons to be * from a * surface. This is called the *.

Answer 12

Heinrich Hertz
ultraviolet , emitted, metallic
photoelectric effect

Question 13

Two experimental observations of the photoelectric effect are in stark contrast with classical wave theory of light.
1. The * of the electrons is independent of the * of the incident radiation.
• Classical physics predicts that the kinetic energy of the emitted electrons should be proportional to the intensity of the incident radiation.
2. There is a * characteristic of the metallic surface, below which no electrons are rejected.
• Classical physics predicts that the photoelectric effect should occur for any frequency of light with sufficient intensity.

Answer 13

kinetic energy, intensity

threshold frequency

Question 14

Photoelectric Effect and Albert Einstein
In order to explain these results, Albert Einstein used Planck’s hypothesis, and
extended it in an important way.
• Planck applied his quantization concept to the * of electronic oscillators. Once the light was emitted, it behaved like a classical wave.
• Einstein proposed that the radiation itself existed in small *, e = hv, also known as *.

Answer 14

emission and absorption mechanism
packets of energy
photons

Question 15

Einstein showed that the kinetic energy of the ejected electron is related to the incident radiation and the work function of the metal (f, similar to the
ionization energy)

Answer 15

KE = E(hv) of incident radiation - work function

Question 16

Balmer Series for Hydrogen Atoms
Emission spectrum of Hydrogen
Johannes Rydberg accounted for all the lines in the hydrogen atomic spectrum by
generalizing the Balmer formula to:

Answer 16

𝟏/𝝀 = R (𝟏/(𝒏𝟏)^𝟐 − 𝟏/(𝒏𝟐)^2)

Question 17

In 1913, Niels Bohr explained the * by assuming Planck’s idea of energy being quantized.

Answer 17

line spectra

Question 18

Niels Bohr assumed that the * of the electron in a hydrogen atom is quantized.
• Classical physics predicts that an electron revolving around a nucleus will lose energy and spiral into the nucleus, and so a stable orbit of the electron is
classically forbidden.
• Bohr first assumed the existence of stationary electron orbitals.
• He then specified these orbits by invoking a quantization condition, and assumed that the angular momentum of the electron must be *

Answer 18

angular momentum

quantized

Question 19

*series occurs at

n = 1, the * series at n = 2, * series at n = 3

Answer 19

Lyman, Balmer, Paschen

Question 20

In 1924, Louis de Broglie introduced his theory of *, based on the work of Max Planck and Albert Einstein on light. This theory stated that that any * or object had an associated *.

Answer 20

wave-particle duality theory of matter

moving particle, wave

Question 21

Experiments on the properties of light
• The * is an example of the
wavelike property of light.
• The * is an example of the particlelike property of
light, that is, behaving as a stream of *.

Louis de Broglie reasoned that if light can display this wave-particle duality, then matter might also display wavelike properties under certain conditions.

Answer 21

dispersion of white light into its spectrum by a prism
photoelectric effect
photons

Question 22

Einstein had shown from relativity theory that the momentum of a photon is:
De Broglie argued that both light and matter obey the equation:

Answer 22

p = h/wavelength (y)

de Broglie wavelength = h/p = h/mv

Question 23

This equation predicts that a particle of mass m moving with a velocity v will have a de Broglie wavelength .
• He called the waves associated with material particles *.
• This theory was confirmed by * experiments.

Answer 23

matter waves

electron diffraction

Question 24

Bohr model of the Hydrogen atom
1. The electron moves in * about the nucleus with motion described by classical physics.
2. The electron has only a *
set of orbits (specific/quantized *). 
3. An electron can only pass from
one orbit to another.

Answer 24

circular orbits

fixed discrete, energy values

Question 25

energy of an electron occupying an orbit

one-electron atom

Answer 25

E = (-RH/n^2)
for one electron-atom:
E = (-Z^2Rh)/n^2

Question 26

State the series + type of ER
nf = 1
nf = 2
nf = 3
nf = 4

Answer 26

1, lyman series (UV)
2, balmer series (visible light)
3, Paschen series (near IR)
4, Brackett series (IR)

Question 27

Failure of Bohr’s model:
1) It cannot predict energy levels for *
atoms.
2) The fixed-orbit model is inconsistent with classical
electromagnetic theory. Any orbiting charge must
constantly emit radiation, decrease its energy, approach
closer to the nucleus and eventually crash into it!
(does not take into account electron as a
*)

Answer 27

multi-electron

wave

Question 28

Electrons have wave-like properties as shown by *experiments

Answer 28

Davisson/Germer electron diffraction by metal crystal

electron diffraction by GP Thomson

Question 29

“The position (x) and momentum (p) cannot be measured with great precision simultaneously.”
Equation:
This led to the probabilistic interpretation of quantum mechanics.

Answer 29

Heisenberg’s (1920)
UNCERTAINTY PRINCIPLE
Δ𝒙 Δ𝒑 ≥ 𝒉/𝟒𝝅

Question 30

The * is an equation of motion of particles (like electrons) that account for their wave-like properties

Answer 30

SCHRÖDINGER equation

Question 31

electrons do not revolve in an orbit but
roam around a defined *
around the nucleus which differs depending on the
amount of * the electron has

Answer 31

region of 3D space,

energy

Question 32

Solving the SCHRÖDINGER equation
provides values for En and 𝜳(r, 𝜽,𝝓)
A total of * quantum numbers are needed
to describe a wavefunction in *

Quantum numbers (n, l, ml) naturally arise from
the mathematical form of the * for the * atom!

Answer 32

3, 3D

wave function solutions, hydrogen

Question 33

The * 𝛹(r,t) that are solutions to the Schrodinger equations for atoms/molecules are called *

Answer 33

wave functions, orbitals

Question 34

Regions with large |𝜳(r,t)|^2 are regions with *, that is, regions where there is high probability for an electron to occupy.

Answer 34

high probability density

Question 35

From wave mechanic solutions, each 𝛹(r,t) can be assigned three *.

Answer 35

quantum numbers (n, l, ml)

Question 36

All orbitals with the same n belong to the same *.
All orbitals with the same n and l belong to the
same *.
All orbitals in the same subshell/sublevel in a hydrogen atom are * (all equal in energy).

Answer 36

shell, subshell/sublevel, degenerate

Question 37

shell or energy level

Answer 37

principal quantum number

Question 38

subshell or shape of the orbital

Answer 38

angular momentum

Question 39

orbital/spatial orientation

Answer 39

magnetic quantum number

Question 40

In 1920, * demonstrated that electrons have spin, with the following properties:
1) An electron, because of its spin, generates a *
2) A pair of electrons with * spins has no net magnetic field.
3) The direction of the net magnetic field produced depends only on the spin of the * electrons.
4) There is an equal chance that the
spin of the unpaired of electron will
be +1/2 or −1/2.

Answer 40

Otto Stern and Walter Gerlach
magnetic field.
opposing
unpaired

Question 41

The spin quantum number leads to …

Only two electrons may occupy the same orbital, and these electrons must have opposing spins.
Alternatively, In a quantum-mechanical system, no two electrons can have the same *.

Answer 41

Pauli exclusion principle

wave function

Question 42

Quantum mechanics two tenets:

Answer 42

1. Radiation (light) and matter display
both wave-like and particle-like
properties
2. Energy is quantized into discrete
packets (called photons)

Question 43

In * spectroscopy, a sample is allowed to generate its own radiation. Then, it scans at each λ of the emitted radiation and measures its intensity.

In * spectroscopy, radiation is let to pass through a sample. Then, it scans at each λ of the transmitted radiation and measures its intensity.

Answer 43

emission,

absorption

Question 44

Classical theory:
Matter - 
Energy - 
Since matter is discontinuous and particulate, perhaps energy is discontinuous and particulate too
Observations, theories
1. Br
2. Pe
3. As
Since energy is wavelike, perhaps matter is wavelike too
Observation, theory
1. Ed
Since matter has mass, perhaps energy has mass
Observation, theory
1. Pw

Answer 44

matter is particle-like
energy is wave-like
-
Blackbody radiation (Planck: energy is quantized)
Photoelectric effect (Einstein : light exists as a discrete packet of energy called photon)
Atomic spectra: (Bohr: energy of atoms is quantized, photon is emitted when electron changes orbit)
-
Davisson/Germer + GP Thomson electron diffraction (de Broglie: All matter travels in waves: energy of atoms is quantized due to wave motion of electrons)
-
Compton: photon wavelength increases (momentum decreases) after colliding with electron
Einstein/de Broglie: Mass and energy are equivalent. Particles have wavelength and photons have momentum

Question 45

Quantum theory:

Answer 45

energy and matter both have wave-like and particle-like properties.
Energy is quantized