C. Johannesson Ch. 4 - Electrons in Atoms
Section 1 The Development of a New Atomic Model
Objectives
• Explain the mathematical relationship among the speed, wavelength, and frequency of electromagnetic radiation.
• Discuss the dual wave-particle nature of light.
• Discuss the significance of the photoelectric effect and the line-emission spectrum of hydrogen to the development of the atomic model.
• Describe the Bohr model of the hydrogen atom.
C. Johannesson
Electromagnetic Spectrum
LOW
ENERGY
HIGH
ENERGY
Includes all forms of electromagnetic
radiation (energy that exhibits wavelike
behavior as it travels through space)
Waves
Wavelength () - length of one complete wave
Frequency () - # of waves that pass a point during a certain time period hertz (Hz) = 1/s
Amplitude (A) - distance from the origin to the trough or crest
on
EM Spectrum
LOW
ENERGY
HIGH
ENERGY
R O Y G. B I V
red orange yellow green blue indigo violet
LONG
WAVELENGTH
EM Spectrum
Frequency & wavelength are inversely proportional
c = c: speed of light 3.00 108 m/s (in a vacuum): wavelength (m, nm, etc.): frequency (Hz)
EM Spectrum
GIVEN:
= ?
= 434 nm = 4.34 10-7 m
c = 3.00 108 m/s
WORK: = c
= 3.00 108 m/s 4.34 10-7 m
= 6.91 1014 Hz
EX: Find the frequency of a photon with a wavelength of 434 nm.
Click below to watch the Visual Concept.
Visual Concept
Energy of a Photon
Electrons as Waves
EVIDENCE: DIFFRACTION PATTERNS
ELECTRONSVISIBLE LIGHT
•Electrons, like light waves, can be bent, or diffracted.
•Diffraction refers to the bending of a wave as it passes by the edge of an object or through a small opening
Bohr Model of the Hydrogen Atom
• Niels Bohr proposed a hydrogen-atom model that linked the atom’s electron to photon emission.
• According to the model, the electron can circle the nucleus only in allowed paths, or orbits.• Electrons are allowed to exist in any one of
a number of energy levels (lowest energy state is closest to the nucleus)
• Only worked for Hydrogen (1 electron)
Click below to watch the Visual Concept.
Visual Concept
Bohr Model of the Atom
Planck (1900)
Observed - emission of light from hot objects
Concluded - energy is emitted in small, specific amounts (quanta) not continuously as expected by energy in the form of waves
Quantum - minimum amount of energy that can be lost or gained by an atom
Quantum Theory
Einstein (1905)
Observed - photoelectric effect- emission of electrons from a metal when light shines on the metal
Einstein (1905)
Concluded - light has properties of both waves and particles
“wave-particle duality”
Photon - particle of light that carries a quantum of energy
Line-Emission Spectrum
Each element has a unique bright-line emission spectrum. Hydrogen always produced same line-emission spectrum
so releases (emission) energy of only certain values
“Atomic Fingerprint”
Helium
Line-Emission Spectrum Cont…
ground state- lowest energy state
of an atom
excited state- state in which an atom has a higher potential energy than its ground state
ENERGY IN PHOTON OUTLine –emission spectrum is
caused by energy released
when electrons “jump from
higher energy to lower
energy
Quantum Mechanics
Heisenberg Uncertainty Principle
Impossible to know both the velocity and position of an electron (small particle) at the same time
Quantum theory describes mathematically the wave properties of electrons and other very small particles.
Quantum Mechanics
• Electrons do not travel around the nucleus in neat orbits, as Bohr had postulated.
• Instead, they exist in certain regions called orbitals.
• Orbital (“electron cloud”)
Region in space where there is 90% probability of finding an e- three-dimensional space
Orbital
C. Johannesson
Quantum Numbers
UPPER LEVEL
Four Quantum Numbers:
Specify the “address” of each electron in an atom
Specify properties of the atomic orbitals and properties of electrons in it
Quantum Numbers
1. Principal Quantum Number ( n )
Energy level
Size of the orbital
n2 = # of orbitals in the energy level
As n increases, e- energy and distance from nucleus increases
Quantum Numbers
s p d f
2. Angular Momentum Quantum # ( l )
Energy sublevel
Shape of the orbital
Number of orbital shapes
possible equal to n
Quantum Numbers
n = # of sublevels per level
n2 = # of orbitals per level
Sublevel sets: 1 s, 3 p, 5 d, 7 f
Quantum Numbers
3. Magnetic Quantum Number ( ml )
Orientation of orbital
S-1, p-3,d-5, f-7
Specifies the exact orbitalwithin each sublevel
Quantum Numbers
4. Spin Quantum Number ( ms )
Electron spin +½ or -½
An orbital can hold 2 electrons that spin in opposite directions.
As it spins creates a magnetic field
Quantum Numbers
Pauli Exclusion Principle
No two electrons in an atom can have the same 4 quantum numbers.
Each e- has a unique “address”:
Electron Configuration
Arrangement of electrons in an atomAtoms of different elements have different
numbers of e-, a distinct electron configuration exists for atoms of each element
e- in atoms tend to assume arrangements that have lowest possible energies (ground-state)
General Rules
Aufbau Principle
Electrons fill the lowest energy orbitals first.
“Lazy Tenant Rule”
Energies of sub-levels begin to overlap
4s is lower in energy than 3d
RIGHTWRONG
General RulesHund’s Rule
Within a sublevel, place one e- per orbital before pairing them.
Separating unpaired electrons into as many orbitals as possible minimizes the repulsion between electrons
Shorthand Configuration
S 16e-
Valence Electrons
Core Electrons
S 16e- [Ne] 3s2 3p4
1s2 2s2 2p6 3s2 3p4
Notation
Longhand Configuration
1
2
3
4
5
6
7
Periodic Patterns
Shorthand Configuration/Nobel Gas Notation
Core e-: Go up one row and over to the Noble Gas.
Valence e-: On the next row, fill in the # of e- in each sublevel.