CH 2.1-2.5 Flashcards
Henry Moseley
Found that protons identify the atom, not the atomic mass
- Used X-ray scattering & built an instrument to measure the charge of the nucleus & confirm the existence of electrons
- looked at the pattern of the wavelengths, tried to plot it linearly but then plotted the square root of the frequency (it was linear)
- Concluded that the atomic # = + charge on nucleus
- ordered 92 elements
Equation for speed of light
Speed of light (cycles) = wavelength (meters) x frequency (cycles per second, hertz)
The wave nature of light
- electromagnetic waves originate form the movement of electric charges
- movement produces fluctuations in electric & magnetic fields
- electromagnetic waves require no medium
- electromagnetic radiation is characterized by its wavelength, frequency, & amplitude
Wavelength
Distance btwn 2 peaks or troughs in a wave (consecutive cycles)
Frequency
Points to the number of waves (cycles) per second that pass a given point in space
- Unit = waves/s or s^-1 (hertz)
Speed
Constant, height of wave
- Speed of light = 2.9979 x 10^8
Amplitude
- Indicates field strength
Standing waves
Stationary (waves don’t travel along the length of the string) waves moving up & down
- The electron in the hydrogen atom is considered to be a standing wave
- Like musical instruments
What is the relationship between wavelength & frequency?
They are inverses of each other
- increase in frequency = decrease in wavelength & vice versa
James Clerk Maxwell
- predicated the existence of invisible “light” waves
- Radio waves reflect & refract just like light
- light travels @ a constant speed
- Paradigm: light is an electromagnetic wave
Heinrich Hertz
- detected radio waves
Refract
Going through different mediums
Diffract
Waves spread out when they encounter an obstacle about the size of the wavelength
- produces constructive & destructive interference
Who showed that light could be diffracted
Thomas Young
Colors in order from shortest wavelength to longest
VBGYOR
Types of waves in order of least to greatest wavelengths
Gamma rays
X rays
Ultraviolet
Infrared
Microwave
Radio
Isaac Newton
- Law of Gravitation
Black body
An ideal object that absorbs all incident EM radiation, regardless of frequency or angle of incidence (can also emit radiation- continuous spectra)
- as it is heated, it glows more brightly, giving changes from red through orange & yellow toward white as it gets hotter
- doesn’t favor one wavelength over the other
- Colors correspond to the range of wavelengths radiated by the body at a given temp
Stefan-Boltzmann Law
Total intensity of radiation emitted by a black body over all wavelengths proportional to T^4
- based on experimental measurements by Tyndall
Ultraviolet Catastrophe
EM Paradigm. Cannot explain the wavelength dependence of the intensity of the light that is emitted from a simple heated object
Max Planck
Explains the ultraviolet catastrophe by quantizing the energy of light
- E = hv
- proposed that exchange of energy btwn matter & radiation occurs in packets of energy called QUANTA
- h = Planck’s constant 6.626 x 10^-34 Jxs
- Radiation of frequency (v = E/h) is emitted only if enough energy is available
- energy can only be gained or lost only in whole-number multiples of hv
- implies that energy has particulate properties
- concept completely disregarded classical physics
Change in energy equation
Delta E= nhv
- n is an integer
- h is Planck’s constant
- v represents the frequency of EM radiation
Quanta
Discrete amount of energy
The photoelectric effect
The phenomenon whereby electrons are emitted from the surface of a metal when light strikes it
- No electrons emitted by any given metal below a specified threshold frequency, v0
- When v is LESS than v0, no electrons are emitted, regardless of the intensity of light
- When v is GREATER than v0, the # of electrons increases with the intensity of light
- When v is GREATER than v0, the kinetic energy of emitted electrons increases linearly with the frequency of the light
- The current of photoelectrons, when it exists, is proportional to the intensity of the light falling on the surface
- The energy of the photoelectrons emitted is independent of the light intensity but varies linearly with the light frequency
- facts cannot be explained within framework of classical physics
Electromagnetic radiation
Radiant energy that exhibits wavelike behavior & travels through space at the speed of light in a vacuum
Three primary characteristics of waves
wavelength, frequency, speed
Particles
Things that had mass & whose position in space could be specified
Waves
Massless & delocalized
What did scientists believe about particles & light before the 1900s?
There was no intermingling of matter & light
Quantum
Small “packets” of energy that is quantized in units of hv
Photon
A quantum of electromagnetic radiation
Albert Einstein
Suggested that electromagnetic radiation can be viewed as a stream of “particles” called photons
- Special Theory of Relativity; E=mc^2; states that energy has mass
- Proposed that light of fixed frequency (v) consists of a collection of indivisible discrete units called quanta
- applied Planck’s quantum theory (photos)
Kinetic energy of electron equation
KE = 1/2mv^2 = hv - hv0
- m= mass of electron
- v= velocity of electron
- nu=energy of incident photon
- hv0= energy required to remove electron from metal’s surface
Energy of photon equation
Energy of photon = hc/wavelength
Apparent mass of a photon of light equation
m = E/c^2 = (hc/wavelength)/c^2 = h/(wavelength x c)
Dual nature of light
The statement that light exhibits both wave & particulate properties
De Brogile’s equation
wavelength = h/(m x v)
- h = Planck’s constant
- m = mass
- v = velocity of particle
- calculate wavelength for a particle
Constructive diffraction
Scattered light produces a bright area
- peaks & troughs of the beams are in phase
Destructive diffraction
Scattered light produces a dark spot
- peaks & troughs are out of phase
- decreased intensity
Excited atoms
Atoms that contain excess energy, which they release by emitting light of various wavelengths to produce the EMISSION SPECTRUM of the hydrogen atom
Continuous spectrum
A spectrum that exhibits all the wavelengths of visible light and results from white light passing through a prism
Line spectrum
A spectrum showing only certain discrete wavelengths
- aka hydrogen emission spectrum
Significance of the line spectrum of hydrogen
It indicates that only certain energies are allowed for the electron in the hydrogen atom
- Energy of the electron in the hydrogen atom is quantized (ties in w/Planck)
Niels Bohr
Developed quantum model of H atom
- proposed that the electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits (calculated radii for these orbits)
Dobereiner’s Triads
- suggest a underlying pattern in elements with respect to atomic mass
What did the Chemicall Congress of 1860 debate in 1860
- Whether to use chemical equivalents or atomic weights to describe chemical reactions
- What symbolism to use for chemical formulas
S. Cannizzaro
Wrote pamphlet that distinguished btwn atoms & molecules
- based his suggestions on Avogadro’s hypothesis
Cannizzaro principle
The atomic weight of an element is the least weight of it contained in a (volatile) molecule
- Established H as diatomic, as well as O
John Newlands
- First law abt the periodicity of the elements was formulated around the US Civil War (1865)
- Using the atomic weights from Cannizzaro, he divided the 56 known elements into 8 groups, based on atomic weights & characteristics (his original had 7 groups)
- rule of octaves
Rule of Octaves
- Increases occur after each interval of 7 elements
Who were the 2 scientists that independently discovered the “modern” Periodic Table in 1869
Lothar Meyer & Dimitri Mendeleev
Dimitri Mendeleev
Listed elements for the Periodic Table based on their respective atomic weights
- states there are missing elements
8 statements Mendeleev made about his Periodic Table
- When arranged by atomic weight, elements show a periodicity of properties
- Similar elements have atomic weights which are either very similar or which increase regularly
- The arrangement of the elements correspond to their valences
- Elements which are most common have small atomic weights
- The atomic weight can determine the character of an element
- More elements will be discovered
- The atomic weight of an element may be corrected by comparison with adjacent elements
- Some properties of unknown elements can be predicted from their atomic weights
Energy levels available to the electron in the hydrogen atom
E = -2.178 x 10^-18 J (Z^2/n^2)
- N = integer, (the larger the n, the larger the orbit radius)
- Z = nuclear charge
- negative charge= energy of the electron bound to the nucleus is lower than it would be if the electron were at an infinite distance
Electron is at an infinite distance from the nucleus
- No interaction & 0 energy
E= -2.178 x 10^-18 J (Z^2/(inf^2))= 0
The more tightly held (closer to the nucleus) the electron in the hydrogen atom is, the more _______ its energy
negative
Equation for change in energy of an electron when the electron changes orbits
E = -2.178 x 10^-18 J (Z^2/n^2)
- N = integer, (the larger the n, the larger the orbit radius)
- Z = nuclear charge
- > # = more negative energy
Equation for change in energy
Energy of final state (J) - energy of initial state (J)
- negative sign = atom lost energy
Equation for wavelength of emitted photon
- Change in energy = h (c/wavelength)
- wavelength = hc/change in energy
2 important points about the Bohr Model
- The model correctly fits the quantized energy levels of the hydrogen atom & postulates only certain allowed circular orbits for the electron
- As the electron becomes more tightly bonded, its energy becomes more negative relative to the zero-energy reference state (corresponding to the electron being at infinite distance from the nucleus). As the electron is brought closer to the nucleus, energy is released from the system
Did Bohr’s model apply to atoms other than hydrogen?
No
Do electrons move around the nucleus in circular orbits?
no
Louis de Brogile
originated the idea that the electron shows wave properties
- says bohr model assumes an electron is a particle
What did both Schrodinger and de Brogile notice
The electron bound to the nucleus seemed similar to a standing wave. They began research on a wave mechanical description of the atom
Schrodinger’s equation
Hψ = Eψ
- H = set of mathematical instructions called an operator
- ψ = wave function
- E = total energy of atom (potential energy due to the attraction btwn the proton & electron + KE of moving electron)
wave function
Function of the coordinates (x,y,z) of the electron’s position in 3D space
- function of position and time
- contains all information there is to know about the particle
operator (H)
Contains mathematical terms that produce the total energy of the atom when they are applied to the wave function
Orbital
A specific wave function for an electron in an atom
What does the square of ψ give?
The probability distribution of finding an electron near a particular point in space
Quantum (wave) mechanical model
A model for the hydrogen atom in which the electron is assumed to behave as a standing wave
1s orbital
Lowest energy wave function (orbital)
- Its electrons are NOT moving around the nucleus in a circular orbit
Does the wave function give us any info about the detailed pathway of the electron?
No
Heisenberg Uncertainty Principle
States that there is a fundamental limitation to how precisely both the POSITION and MOMENTUM of a particle can be known at a given time
Heinsberg Uncertainty Principle Equation
Δx x Δ(mv) is greater than or equal to (h/(4π)
- Δx = uncertainty in a particle’s position
- Δ(mv) = uncertainty in a particle’s momentum
- h = Planck’s constant
- (h/(4π) = minimum uncertainty in the product
In simple terms, what does the Heinsberg Uncertainty Principle say?
The more accurately we know a particle’s position, the less accurately we can know its momentum and vice versa
N1/N2
[(ψ (x1,y1,z1))^2/ (ψ (x2,y2,z2))^2] = N1/N2
- Ratio of probabilities of finding the electron at positions 1 & 2
Does Heinberg’s Uncertainty model give an info concerning when the electron will be at either positon or how it moves btwn the positions ?
No
Probability Distribution
Square of wave function indicating the probability of finding an electron at a particular point in space
- Intensity of color is used to indicate the probability value near a given point in space
Electron Density/Probability Map
The more times the electron visits a particular point, the darker the image becomes
Radial Probability Distribution Graph
The total probability of finding the electron in each spherical shell is plotted V.S. the distance from the nucleus
The probability of finding an electron at a particular position is ____ near the nucleus, but the volume of the spherical shell _____ with distance from the nucleus
Greatest, increases
For the hydrogen 1s orbital, the maximum radial probability (the distance at which the electron is most likely to be found) occurs at a distance of ____
5.29 x 10^-2 nm
- exact same radius of the innermost orbit in the Bohr model
Definition most used by chemists to describe the size of the hydrogen 1s orbital
The radius of the sphere that encloses 90% of the total electron probability
Differences btwn Mendeleev & Meyer
Mendeleev
1. didn’t concern himself w/why the table worked
2. thought elements were primordial matter
3. continued to work on his table & was recognized quickly
Meyer
1. Not as daring, very reflective with internal structure
2. thought there must be yet smaller particles
3. Took decades for others to understand his work of the inner structure of an atom
Classical Electromagnetic Theory
An accelerated electric charge radiates (loses) energy (electromagnetic radiation) which means total energy must decrease
Key equations
c = lambda x nu
c = speed of light
lamba = wavelength
nu = frequency
P. Lenard
Discovered the Photoelectric Effect
Equation for kinetic energy of electron that is emitted
K = hv - W
- W = lowest energy needed to remove an electron = E0 = hv0
Energy brought by photon (hv) broken down
E= hv
E= K (electron, 1/2 x m sub e x v^2) + Energy needed to remove electron (threshold energy)
Photoelectric Effect Graph
- Kinetic energy of ejected electron = y-axis
- frequency of incident radiation = x-axis
- slope = h
- intercept with v-axis = W/h
Planck’s quantum hypothesis
States that energy can be absorbed or emitted only as a quantum or whole multiples of a quantum, thereby making variations of energy DISCONTINUOUS
- Changes in energy can occur only in DISCRETE amounts
Basis of Quantum Mechanics
It is impossible to determine simultaneously both the position & momentum (velocity) of an electron (or any other small particle)
- The more we know about where an electron is (position), the less we know about where it is going (momentum)
- changes in energy is not continuous
Schrodinger
if electrons are waves, their position & motion in space must obey a wave equation
- proposes electron wave functions are standing waves
Stable standing waves has to have….
a wavelength in multiples that must fit into the circumference of an atom (2pir)
Copenhagen Interpretation of Quantum Mechanics
- A system is completely described as ψ
- The description of nature is probabilistic
- Those properties that are not known with precision must be described by probabilities
- Matter exhibits a wave-particle duality
- measuring devices are essentially classical devices
- the quantum mechanical description of large systems will closely approximate the classical description
ψ^2
probability distribution of finding electron around the nucleus
