Chapter 7: Quantum Mechanics Flashcards
What doe the wave equation apply to?
It applies to any measured value that is a function of position at a given time or to any measured value that is a function of time at a given position.
What is the name and symbol for the distance between two adjacent crests peaks (or any two analogous points) on a wave?
Wavelength - λ (lamda)
What is the name and symbol for the time between the two peaks, or the time it takes to complete one cycle?
Period - T
Frequency, symbol _____, is inversely proportional to _____.
v
T
(so V= 1/T)
When wave moves does any matter actually change position when referring to light or sound waves?
No matter changes position, only the crest (or any other point on the wave), appears to change position.
What is phase velocity?
The velocity at which the trough (or peak, or other) appears to move
Phase velocity is proportional to _____ and inversely proportional to _____.
wavelength (λ)
period (T)
(phase velocity=λ/T)
Phase velocity is proportional to ____ and ____.
wavelength (λ)
Frequency (ⱱ)
(phase velocity=λ∙ⱱ)
What is the phase velocity of electromagnetic radiation (light in particular)?
3.00 x 10^8 m/s
In which region of the electromagnetic spectrum does light exist?
From λ 400 nm to 750 nm
λ 400nm is ____ light
voilet
λ 750nm is ____ light
red
Is it possible to measure the frequency of lIght? If not how do we figure it out?
No, though we can calculate it multiplying the wavelength and phase velocity
How do we measure the wavelength of light?
Through constructive and destructive interference
Constructive interference occurs when the waves are ______ phase.
Destructive interference occurs when waves are _____ phase.
in
out of
In the double slit experiment what occurs in the halfway point between the two slits?
A bright spot
Why does a bright spot occur halfway between the two slits in the double slit experiment?
It occurs because at this point both of the waves travelling from the slit have traveled the same distance, and because they both have the same source and therefore wavelength, constructive interference occurs and the light therefore appears brighter
As you travel away from the halfway point in the double slit experiment what pattern occurs and why?
A pattern of light and dark occurs, this is because when you move away the length the wave has to travel increases for one and decreases for the other so the are either in or out of phase, due to the length the wave must travel. this creates alternating constructive and destructive interference.
What does the quantum-mechanical model of the atom explain?
It explains how electrons exist in atoms and how those electrons determine the chemical and physical properties of elements
What common characteristic do both light and electrons share?
Wave -particle duality
What is electromagnetic radiation?
A type of energy embodied in oscillating electric and magnetic fields
Light is…..?
Electromagnetic radiation
What is an electric field?
A region of space where an electrically charged particle experiences a force
What is a magnetic field?
A region of space where a magnetic particle experiences a force
How can you best describe the way an electromagnetic radiation wave is composed?
Electric and magnetic fields that are Oscillating, mutually perpendicular, and propagating through space
What is the amplitude of a wave?
The height of a crest or the depth of a trough
What does the amplitude of the electric and magnetic fields of a wave of light determine?
It determines the lights intensity (or brightness)
The amplitude is proportional to the intensity
What SI units are wavelengths measured in?
Meters
A wave with the ______ amplitude and _____ wavelength will result in the most energetic wave.
Largest
Shortest
A wave with the ______ amplitude and _____ wavelength will result in the least energetic wave.
Smallest
Longest
What is frequency(v)?
The number of cycles (or wave crests) that pass through a stationary point in a given period of time.
What three main things are used to characterize light?
Wavelength
Amplitude of the wave
Frequency
What are the units for frequency?
Cycles per second or s^-1 or hertz (Hz)
Frequency is directly proportional to _____ and inversely proportional to ____. So therefore in the case of light which formula can be used?
The speed at which the wave is traveling
The wavelength
v=c/λ
For visible light what factor determined the colour of the light?
Wavelength (or alternately frequency)
How does a wave diffract?
A wave diffracts when it encounters an obstacle or slit that is comparable in size to its wavelength
What is the photo electric effect?
The observation that metals can emit electrons when light shines Upon them.
How does light cause a electron to be emitted from a metal?
It occurs due to a high energy photon having enough energy to dislodge the electron as well as transfer more energy onto the electron in the form of kinetic energy
Does increasing the intensity of the light increase the energy of the photons?
No
Does increasing the frequency of the light increase the energy of the photons?
Yes
What is atom spectroscopy?
The study of the electromagnetic radiation absorbed and emitted by atoms
When an atom absorbs energy (in the form of heat, light, or electricity) it often emits that energy as _____
Light
What is the emission spectrum?
The range of wavelength emitted by a particular elements; used to identify an element
In the double slit experiment what is the bright spot in the halfway points between the two slits called?
zero order
from there on they are called 1st order then 2nd order and so on and so forth
In the double slit experiment if we change the wavelength of the light what also changes?
the distance between the bright spots.
λ ∝ distance between bright spots
In the double slit experiment if the screen is far from the slits the distance between bright spots will be much ____ than λ
much larger
Which equation did scientists discover to be true when an atom emits or absorbs light?
ΔEatom = ±hⱱ
ofs
If light is absorbed by an atom then ΔEatom is _____ than zero
greater
If light is emitted by an atom then ΔEatom is _____ than zero
less
what value does h the constant in ΔEatom = ±hⱱ have? and what is the name of this constant?
h = 6.626 x 10^-34 J∙s (ofs)
plancks constant
What equation do we call Photon energy?
Ephtoton = hⱱ
When an atom absorbs energy (light) what occurs?
an electron is being excited
If enough energy is applied to an atom what can occur?
the electron is excited so much that it has enough energy to escape the atom and so it ejects into space
When an atom escapes into space after exceeding the binding energy what does its energy become?
kinetic energy
What other two names is the binding energy referred to by?
threshold energy and work function
what is the binding energy?
the amount of energy is takes for an electron to escape the atom
The transitions between levels that are farther apart in energy produce light that is ______ in wavelength
Shorter
The transitions between levels that are closer together in energy produce light that is ______ in wavelength
Longer
Which ions is the Bohr theory successful in explaining the spectra of?
Hydrogen like ions (only have one electron)
ΔE= -2.18 x 10⁻¹⁸ J (Z²/nf² - Z²/ni²) what does the Z mean?
Z is the atomic number
When an electron transitions between stationary states in a hydrogen atom what causes the transition to be unlike any macroscopic transition?
The electron is NEVER observed between states (the transition is instantaneous)
Why does the emission spectrum of an atom consist of discrete lines?
Because the stationary states only exist at specific, fixed energies
What is the energy of the photon created when an electron makes a transition from one stationary state to another?
The difference in energy between the two stationary states
Transitions between stationary states that are closer together produce light of a _____ energy (_____ wavelength) than transitions between stationary states that are farther apart
Lower
Longer
What causes the interference patterns of electrons?
Single electrons interfering with themselves (not electrons interfering with each other)
What important conclusion was made about the wave nature of electrons and what does it explain?
The wave nature of electrons is an inherent property of individual electrons and it explains the existence of of stationary states and prevents the electrons in an atom from crashing into the nucleus
What is the de Brogile relation?
λ = h/ mv
Does light make up a large portion of the electromagnetic spectrum?
No it makes up a very small portion
What range of wavelengths does the electro magnetic spectrum span over?
10^-15 to 10^5 m
What wave on the electromagnetic spectrum has the highest frequency and shortest wavelength?
Gamma rays
What wave on the electromagnetic spectrum has the lowest frequency and longest wavelength?
Radio waves
Planck assumed that energy was emitted in discrete packets called ____ in order to obtain agreement with the black body radiation curve.
Quanta
Albert Einstein called packets of light ____
Photons
Increasing the frequency of light ____ the energy of the photons
Increases
Increasing the intensity of the light _____ increase the energy of the photons
Does not
When an atom absorbs energy - in the form of heat, light or electricity - what often occurs?
The atom re emits that energy as light
What can the emission spectrum of an atom be used to identify?
It can be used to identify the element
Why does the emission spectrum of an atom consist of discrete lines?
Because the stationary states only exist at specific, fixed energies
What does each wavelength in the emission spectrum of an atom correspond to?
It corresponds to an electron transition between two energy levels
what causes an atom to emit light?
When an atoms absorbs energy, an electron in a lower energy level is excited (or promoted), to a higher energy level. This state however is unstable and the electron will quickly fall back (or relax) to a lower energy level. as the electron relaxes it releases a photon of light
What nature is the velocity of an electron related to?
Wave nature
WhAt nature is the position of an electron related to?
Particle nature
Does observing an event affect the outcome?
Yes
What does Heisenberg’s uncertainty principle state?
It states that the product of Δx and mΔv must be greater than or equal to a finite number (h/4π)
The more accurately you know the position of an electron the _____ accurately you know the velocity of the electron and ____ ____
Less
Vice versa
An electron is observed as either a wave ___ a particle, but…
Or
But never both at once
Electrons are indeterminate because???
Even if a electron was shot from the same place every time in the exact same way it would never hit the same spot twice
For electrons which two properties are complementary to position?
Velocity and energy
Why do we say that electrons are in certain orbital instead of giving their position?
Because energy and position are complementary and orbitals are not position but well defined energy
what is the general form of the schrodinger equation?
Hѱ=Eѱ
What is the symbol for wave function?
ѱ
What three interrelated quantum numbers is each orbital specified by?
Principle quantum number, n
Angular momentum quantum number (sometimes called azimuthal quantum number), l
Magnetic quantum number, mı
SUBSCRIPT L
What is the principle quantum number (n) ?
It is an integer that determines the overall size and indicates the energy level of an electron in an orbital.
(Values n: 1,2,3….)
What is the Rydberg constant for hydrogen?
2.18 x 10^-18 J
What is the angular momentum quantum number (L)
It is an integer that correspond primarily with the shape of the orbital
What is the magnetic quantum number (ml)?
It is an integer which specifies the orientation of the orbital
Each specific combination of n, l, ml specifies
One atomic orbital
Orbitals with the same value of n are said to be in the same _______ or _______
Principle level
Principle shell
Orbitals with the same value of n and l are said to be in the same _____ or ______
Sublevel
Subshell
The number of sublevels is equal to…
The principle quantum number (n)
The number of orbitals in any sublevel is equal to…
2 l + 1
The number of orbitals in a level is equal to…
n²
The 1s orbital is the ____ energy orbital. It is _____ _____.
Lowest
Spherically symmetrical
What does the three dimensional plot of the wave function represent?
Probability density
Probability density is…?
The probability (per unit volume) of finding an electron at a point in space
What is wave function squared is equal to?
Probability density (=probability / unit volume)
As the radius (the distance from the nucleus) increases the probability density ____.
Decreases
What does the radial distribution function represent?
It represents the total probability of finding the electron within a thin spherical shell at a distance r from the nucleus
Total radial probability (at a given r) =…?
(Probability / unit volume) volume of shell at r
A node is a point where the wave function, and therefore the probability density and the radial distribution….
All go through zero
What is a radial node?
A spherical region in which there is zero probability of finding an electron
(Sometimes also called spherical node)
What is an angular node?
A plane or surface where there is zero probability of finding an electron
For any orbital, there are ___ angular nodes
l
Each principle level with n=2 or greater contains ____ ____ orbitals
Three
P
Each principle level with n=3 or greater contains ____ ____ orbitals
Five
D
Each principle level with n=4 or greater has ____ ____ orbitals
7
F
What is known as the phase of a wave?
The sign of the amplitude of a wave - positive or negative
What is electron configuration?
A notation that shows the particular orbitals that are occupied by electrons in an atom
What is the ground state?
The lowest energy state
What is electron spin?
A fundamental property of all electrons that affects the number of electrons allowed in one orbital
What is sublevel energy splitting?
Determines the order of electron filling with in a orbital
In a orbital diagram the direction of the arrow represents what?
Electron spin
Spin is a ____ _____ of all electrons. All electrons have _____ amount of spin
Basic property
The same
The orientation of an electrons spin is _____, with only two possibilities that we can call ____ and ____.
Quantized
Spin up
Spin down
What is the spin of an electron specified by?
A fourth quantum number called the spin number (ms)
What are the possible values of the spin quantum number?
+ 1/2 (spin up)
Or
-1/2 (spin down)
What is the maximum number of electrons an orbital can have?
2
With opposing spins
In general, the ____ the value of l within a principle level, the lower the energy of the corresponding orbital
Lower
What are the three key concepts ascociated with the energy of an electron in the vicinity of a nucleus?
(1) coulumbs law, which describes the interactions between charge particles
(2) shielding, which describes how one electron can shield another electron from the full charge of the nucleus
(3) penetration, which describes how one atomic orbital can overlap spatially with another, thus penetrating into a region that is close to the nucleus (and therefore less shielded from nuclear charge)
What is coulombs law?
The potential energy (E) of two charge particles depends on their charges (q1 and q2) and on their separation (r)
(ΔEp=(kq1q2)/r)
For like charges, the potential energy is ____ and ____ as the particles get father apart (as r increases). Since systems tend toward _____ potential energy, like charges ____ each other.
Positive
Decreases
Lower
Repel
For opposite charges, the potential energy is ____ and becomes more _____ as the particles get closer together (as r decreases). Therefore opposite charges ____ each other
Negative
Negative
Attract
The magnitude of the interaction between charged particles _____ as the charges of the particles increase
Increases
If there is only one electron in an ion or atom the 2s and 2p orbitals _____.
Degenerate
What is Hunds rule?
Hunds rule states that when filling degenerate orbitals, electrons fill them singly, with parallel spins
As we move right across a row of transition elements, electrons are added to the (n-1) d orbitals where n is…?
The row number in the periodic table and also the quantum number of the highest occupied principle level
What is paramagnetic?
The state of an atom or ion that contains unpaired electrons and is, therefore, attracted to an external magnetic force
What is diamagnetic?
The state of an atom or ion that contains only paired electrons and is, therefore, slightly repelled by an external magnetic field
What is the form of electromagnetic radiation with the shortest wavelength?
Gamma ray
Define interference
Characteristic interaction between waves that can result in the waves cancel it out of building each other up based on their alignment upon interaction
What is constructive interference?
When waves that are in phase combine to make a wave with a greater amplitude
What is destructive interference?
When waves that are out of phase interact to cancel each other out
Define diffraction
The bending of a wave when it encounters an obstacle or slit that is comparable to its wavelength in size
what is the speed of light in a vacuum?
3.00 x 10ˆ8 m/s
you can characterize a wave by its ____ and its ____
amplitude
wavelength
define wavelength
the distance between two adjacent crests (or any two analogous points)
what is the quantum-mechanical model?
a model which explains how electrons exist in an atom and how those electrons determine the chemistry and the physical properties of elements
light was found to have many characteristics in common with _____ and the strongest similar characteristics was the _____ ______ of light
electrons
wave-partical duality
In the double slit experiment the diffraction of light through two slits separated by distance ____ to the ____ of the light, coupled with interference, results in an _____ _____
comparable
wavelength
interference pattern
_____ is a result of the ability of a wave to diffract through two slits —- this is an _____ ____ of light
interference
inherent property
light used to dislodge electrons in the photo electric affect exhibited ____ ___
threshold frequency
in the photo electric affect what occurs when the light was below the threshold frequency?
no electrons were emitted no matter how long the light shone on the metal
______-_____ light does not eject electrons from a metal regardless of its ____ or _____
low-frequency (or long-wavelength)
intensity
duration
why doesnt low frequency light eject electrons?
because no single photon (of low-energy light) has the minimum energy necessary to dislodge the electron
define emission spectrum
the range of wavelengths emittted by a particular element; used to identify the element
when an atom absorbs energy, an electron in a lower energy level is ____ to a ____ energy level. This position, however, is ____ and the electron quickly ___ ___ to a ___ energy level
excited higher unstable falls back lower
transitions between the energy levels of an atom which are father apart produce light that is ____ in wavelength, and therefore higher in ____, than between energy levels that are closer together
shorter
higher
during a transition from energy level to another electrons are NEVER observed _____ _____. the transition is ____
between states
instantaneous
the velocity of a moving electron is related via the de Brogile relation to its _____. so to know one is to know the other
wavelength
what experiment demonstrates that you cannot simultaneously observe both the wave nature and the particle nature of an electron
the single electron diffraction experiment
can you simultaneously observe both particle and wave nature of an electron?
no
define orbital
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
