Quantum Theory and Atomic structures Flashcards
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.
accelerating, emit electromagnetic waves
lose, spiral
highly peaked emission, absorption spectra of atoms
- is a form of energy propagated as mutually * . It includes visible light, infrared,
ultraviolet, X ray, and radio waves.
Electromagnetic radiation
perpendicular electric and magnetic fields
A * is a disturbance that transmits energy through a medium.
wave
- is the height of the crest of a wave above the center line of the wave.
Amplitude
The * is the distance between successive crests or troughs of a wave motion. Designated by lambda.
wavelength
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).
number of wave crests, pass, point, time
distinctive feature of electromagnetic radiation is its constant * of in a
vacuum, often referred to as the speed of light.
speed c = frequency × wavelength
In phase - *
Out of phase - *
Constructive Interference
Destructive Interference
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.
blackbody
frequency
frequency
higher
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 *
Max Planck (1900) radiation, oscillations
energies
integral multiple n, frequency
Planck’s law:
E = nhv
h - 6.626 * 10^-34 J-s
In 1888,* discovered that * light caused electrons to be * from a * surface. This is called the *.
Heinrich Hertz
ultraviolet , emitted, metallic
photoelectric effect
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.
kinetic energy, intensity
threshold frequency
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 *.
emission and absorption mechanism
packets of energy
photons
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)
KE = E(hv) of incident radiation - work function
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:
𝟏/𝝀 = R (𝟏/(𝒏𝟏)^𝟐 − 𝟏/(𝒏𝟐)^2)
In 1913, Niels Bohr explained the * by assuming Planck’s idea of energy being quantized.
line spectra
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 *
angular momentum
quantized
*series occurs at
n = 1, the * series at n = 2, * series at n = 3
Lyman, Balmer, Paschen
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 *.
wave-particle duality theory of matter
moving particle, wave
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.
dispersion of white light into its spectrum by a prism
photoelectric effect
photons
Einstein had shown from relativity theory that the momentum of a photon is:
De Broglie argued that both light and matter obey the equation:
p = h/wavelength (y)
de Broglie wavelength = h/p = h/mv
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.
matter waves
electron diffraction
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.
circular orbits
fixed discrete, energy values
energy of an electron occupying an orbit
one-electron atom
E = (-RH/n^2)
for one electron-atom:
E = (-Z^2Rh)/n^2
State the series + type of ER nf = 1 nf = 2 nf = 3 nf = 4
1, lyman series (UV)
2, balmer series (visible light)
3, Paschen series (near IR)
4, Brackett series (IR)
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
*)
multi-electron
wave
Electrons have wave-like properties as shown by *experiments
Davisson/Germer electron diffraction by metal crystal
electron diffraction by GP Thomson
“The position (x) and momentum (p) cannot be measured with great precision simultaneously.”
Equation:
This led to the probabilistic interpretation of quantum mechanics.
Heisenberg’s (1920)
UNCERTAINTY PRINCIPLE
Δ𝒙 Δ𝒑 ≥ 𝒉/𝟒𝝅
The * is an equation of motion of particles (like electrons) that account for their wave-like properties
SCHRÖDINGER equation
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
region of 3D space,
energy
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!
3, 3D
wave function solutions, hydrogen
The * 𝛹(r,t) that are solutions to the Schrodinger equations for atoms/molecules are called *
wave functions, orbitals
Regions with large |𝜳(r,t)|^2 are regions with *, that is, regions where there is high probability for an electron to occupy.
high probability density
From wave mechanic solutions, each 𝛹(r,t) can be assigned three *.
quantum numbers (n, l, ml)
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).
shell, subshell/sublevel, degenerate
shell or energy level
principal quantum number
subshell or shape of the orbital
angular momentum
orbital/spatial orientation
magnetic quantum number
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.
Otto Stern and Walter Gerlach
magnetic field.
opposing
unpaired
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 *.
Pauli exclusion principle
wave function
Quantum mechanics two tenets:
1. Radiation (light) and matter display both wave-like and particle-like properties 2. Energy is quantized into discrete packets (called photons)
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.
emission,
absorption
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
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
Quantum theory:
energy and matter both have wave-like and particle-like properties.
Energy is quantized
