Quantum Theory and the Electronic Structure of Atoms Flashcards
Max Planck
-discovered that atoms and molecules emit energy only in certain discrete quantities (QUANTA)
-Quantum theory
Classical physics
-energy is continuous and that any amount of energy could be released in a radiation process
-assumed that atoms and molecules could emit or absorb any arbitrary amount of energy
Wave
-vibrating disturbance by which energy is transmitted
-periodic: wave form repeats itself at regular intervals
Wavelength, λ
-distance between identical points on successive waves
Frequence, f
-number of waves that pass through a particular point in one second
1 Hz = 1 cycle/s
Amplitude
-vertical distance from the midline of a wave to the peak or trough
Wave speed, v
-depends on the type of wave and the nature of the medium through which the eave is travelling
v = λ.f
James Clerk Maxwell (1873)
-visible light consists of electromagnetic waves
•Electromagnetic wave- has electric field component and magnetic field; these components have same frequency, wavelength, speed but travel in mutually perpendicular planes
-speed of electromagnetic waves: speed of light
Electromagnetic radiation
-emission and transmission of energy in the form of electromagnetic waves
Gamma rays
-electromagnetic radiation
-shortest wavelength; highest frequency
Radio waves
-electromagnetic radiation
-longest wavelength; lowest frequency
Visible light
-electromagnetic radiation
-wavelength: 400 nm (violet) - 700 nm (red)
⬆️ Frequency ⬆️ Energy
Solids are heated ➡️ emit electromagnetic radiation
Electric heater: dull red
Tungsten light bulb: bright white light
Quantum
-smallest quantity of energy that can be emitted/ absorbed in the form of electromagnetic radiation
-energy of single quantum:
E =h.f
-(Quantum theory): energy is always emitted in multiples of hf (i.e. hf, 2hf, 3hf but not 3.98hf, 1.67hf)
Albert Einstein (1905)
used quantum theory for:
•PHOTOELECTRIC EFFECT
-electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency (threshold frequency)
-no. of electrons ejected proportional to intensity (brightness) of light
-below threshold frequency, no electrons ejected no matter how intense the light
-electrons in metal are held in attractive forces; removing requires light of sufficiently high frequency (~high energy)
Photons- a beam of light is a stream of particles; each photon contains energy
E = h.f
Photoelectric effect formula
hf = KE + BE
KE: Kinetic energy of ejected electron
KE = 1/2 .me. v^2
me: mass of electron
BE: Binding energy of electron in metal
f < fthres : no electron ejected
f = fthres : only knock the electrons loose
f > fthres : electrons knock loose with kinetic energy
-more intense beam of light, larger number of protons: more electrons ejected
-higher frequency of light, greater kinetic energy of emitted electrons
Isaac Newton
-sunlight is composed of various color components that can be recombined to produce white light
Emission spectra
-either continuous or line spectra of radiation emitted by substance
-seen by energizing sample material with thermal energy or some other form of energy
-every element has a UNIQUE emission spectrum
Line spectra
-light emission only at specific wavelength
-emission spectra of atoms in gas phase: do not show continuous spread of wavelengths from red to violet
Niels Bohr (1913)
-emission spectrum of hydrogen atom
-each orbit has a particular energy associated with; energies associated with electron motion in the permitted orbits must be fixed in value or QUANTIZED
-emission of radiation by energized hydrogen atom: associated with electron dropping from higher-energy orbit to a lower one, giving up a quantum of energy (photon) in the form of light
En = -R(1/n^2)
En: energy of electron; n: principal quantum number (1,2,3,4 etc)
Convention: (-) energy of electron in atom is lower than energy of free electron (far from nucleus)
•Free electron: E∞=0
•Electron gets closer to nucleus (n decreases): En = more negative
Ground state/ ground level
n=1
-lowest energy state of a system
Excited state/ excited level
n = 2, 3, 4…
-higher energy than in ground state, less tightly held by nucleus
⬆️ n (farther from nucleus) ⬇️ stability
Rydberg’s formula
∆E = hf = R(1/ni^2 - 1/nf^2)
ni > nf : photon is emitted (-∆E: energy released)
ni < nf : (+∆E: energy absorbed)
Various series in atomic hydrogen emission spectrum
SERIES. nf. ni. Spectrum Region
Lyman. 1. 2,3,4… Ultraviolet
Balmer. 2. 3,4,5… Visible, UV
Paschen. 3. 4,5,6… Infrared
Brackett. 4. 5,6,7… Infrared
Josef Fraunhofer
-studied emission spectrum of the sun and noticed certain dark lines at specific wavelength
-for atoms, emission and absorption of light occur at the same wavelength but differ in appearance.
°Colored lines: emission
°Dark lines: absorption
-matching the absorption lines with emission spectra of known elements: deduce the elements present in stars
Pierre Janssen
-new dark line in solar emission spectrum: Helium
William Ramsay
-discovery of Helium on Earth (in mineral of Uranium)
-only source of Helium: alpha particles emitted during nuclear decay
Louis de Broglie
-if light waves can behave like a stream of particles (photons), particles such as electrons can possess wave properties
-electron bound to nucleus behave like standing/stationary wave
-greater frequency, shorter wavelength, greater number of nodes
•Node: amplitude of the wave at these points is zero
•Standing wave: generated by plucking (i.e. in guitar string)
-waves can behave like particles and particles can exhibit wavelike properties
λ = h/(m.v)
λ: wavelength
h: Planck’s constant
m: mass of moving particle
v: velocity
Laser
-light amplification by stimulated emission of radiation
-special type of emission: involves atoms or molecules
-Ruby laser: first laser
Clinton Davisson, Lester Germer, G.P. Thomson
-electrons do indeed possess wavelike properties
Niels Bohr’s theory limitation
- Did not account for emission spectra of atoms containing more than 1 electron (i.e. Li and He)
- Did not explain why extra lines appear in hydrogen emission spectrum when magnetic field is applied
Electron microscopy
-application of wavelike properties of electrons
-produces images of objects that cannot be seen with naked eye or light microscopes (law of optics: impossible to form image of an object that is smaller than half the wavelength of light used for observation)
Werner Heisenberg
-Heisenberg uncertainty principle: it is impossible to know simultaneously both the momentum p (derined as mass times velocity) and the position of a particle with certainty
∆x∆p => h/(4π)
∆x∆p: uncertainty in mesuring position and momentum
-making measurement of momentum more precise (smaller ∆p), measurement of position of particles less precise (larger ∆x)
-electron does not orbit the nucleus in a well defined path (contradicts Bohr’s theory)
Erwin Schrondiger (1926)
-formulated equarion that describes the behavior and energies of submicroscopic particles in general
-incorporates both particle behavior (mass) and wave behavior (wave function) which depends on the location in space of the system
-probability of finding electron in certain region of space is PROPORTIONAL to square of wave function
-start of QUANTUM MECHANICS field/ wave mechanics
Electron density
-probability that an electron will be found in a particular region of an atom
Atomic orbital
-wave function of an electron in an atom
-has characteristic energy and characteristic distribution of electron density
Quantum numbers
-describe the distribution of electrons in hydrogen and other atoms:
•Principal quantum number
•Angular momentum quantum number
•Magnetic quantum number
°Spin quantum number
-describes the behavior of a specific electron and completes the description of electrons in atoms
Principal quantum number, n
(n = 1,2,3…)
-larger n: greater average distance of an electron in the orbital from the nucleus; larger and less stable orbital
Angular momentum quantum number, l
-Given value of n:
l = 0 to (n-1)
-shape of orbitals; Sharp, Diffuse, Principal, Fundamental … alpha arrange na
s orbital: l=0
p orbital: l=1
d orbital: l=2
f orbital: l=3
g orbital: l=4
h orbital: l=5
Shell
-collection of orbitals with same value of n
Subshell
-one or more orbitals with same n and l values
i.e. n=2; l=0,1
Subshells: 2s subshell and 2p subshell
Magnetic quantum number, msub.l
-orientation of orbital in space
-depends on angular momentum quantum number:
number of msub.l = (2l + 1) orbitals
-l, (-l+1), …, 0, …, (+l+1), +l
•l=0, msub.l=0
•l=1, no. of msub.l=[(2x1)+1]=3
msub.l= -1, 0, 1
Electron spin quantum, msub.s
-electrons act like tiny magnets
-counterclockwise spin: upward arrow
clockwise spin: downward arrow
msub.d = +1/2, -1/2
Otto Stern and Walther Gerlach (1924)
-proof of electron spin:
beam of atoms directed through a magnetic field;
in a stream consisting of many atoms, there will be equal distribution of the two kinds of spin, two spots of equal intensity are detected on screen
Atomic orbitals
-s subshell: 1 orbital (based on number of msub.l)
-p subshell: 3 orbitals
-d subshell: 5 orbitals
S orbital
-spherical shape but differ in size
⬆️ Size ⬆️ Principal quantum number
Boundary surface diagram
-encloses about 90% of the total electron density in an orbital
-electron density falls off rapidly as the distance from the nucleus increases
P orbitals
-start: n=2, l=1, msub.l=-1,0,1
2px, 2py, 2pz
-each p orbital can be thought of as two lobes on opposite sides of nucleus
⬆️ Size ⬆️ Principal quantum number
Energies of orbitals
-orbitals with same principal quantum number,n, have the same energy
⬆️Principal quantum number ⬆️ energy
-1s: closest to nucleus, most strongly held by nucleus, lowest energy
*Remember!!
Direction of electron spin has no effect on the energy of the electron
Electron configuration
n, l, msub.l, msub.s: “address” of electrons
-order in which atomic subshells are filled in a many-electron atom
Pauli Exclusion Principle
Wolfgang Pauli
-determine electron configuration
-no two electrons in an atom can have the same four quantum numbers
-only two electrons may occupy same atomic orbital (each with opposite spin)
Diamagnetic substance ⬆️⬇️
-electron spins are paired/ ANTIPARALLEL to each other; magnetic effects cancel out
-slightly repelled by magnet
-general rule: atoms with EVEN NUMBER OF ELECTRONS- diamagnetic
Paramagnetic substance ⬆️⬆️
-electrons have same/ PARALLEL spins, their net magnetic fields would reinforce each other
-general rule: atoms with ODD NUMBER OF ELECTRONS- paramagnetic
Measurement of magnetic properties
-most direct evidence for specific electron configuration of elements
Shielding effect in many-electron atoms
-i.e. 2s or 2p electron are partly shielded from attractive forces of nucleus by 1s electrons
⬆️Shielding effect ⬇️Electrostatic attraction
-⬇️Penetrating power ⬆️Angular momentum quantum number
s>p>d>f
⬇️Shielding effect ⬆️Penetrating power
Hund’s rule
Frederick Hund
-most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins
(A) |⬆️⬇️| | |
(B) |⬆️ |⬇️ | |
(C) |⬆️ |⬆️ | |
Stability A < B < C
Determination of maximum number of electrons that an atom can have
2n^2
Building-Up Principle/
Aufbau Principle
-protons are added one by one to the nucleus to build up the elements, electrons are similarly added to the atomic orbitals
Noble gas core
-shows in brackets the noble gas element that most nesrly precedes the element being considered
Transition metals
-either gave incompletely filled d susbhells or readily give rise cations that have incompletely filled d subshells
Lanthanides/ Rare Earth Series
-have incompletely filled 4f subshells or readily give rise to cations that have incompletely filled 4f subshells
