Chapter 5 Electrons in Atoms

I. Wave Nature of Light In the early 1900s, scientists observed certain elements emitting visible light when heated Study of the emitted light revealed that an element’s chemical behavior is related to the arrangement of its electrons Electromagnetic radiation is a form of energy that exhibits wavelike behaviors as it travels through space

Increased Energy

Waves have several primary characteristics 1. Wavelength (λ, lambda) Shortest distance between equivalent points on a continuous wave

2. Frequency (ν, nu) Number of waves that pass a given point per second One hertz (Hz) is the SI unit for frequency - one hertz equals one wave per second 652 Hz = 652 waves/second = 652/s = 652s -1 High Frequency Low Frequency

Wavelength and frequency are inversely related - as one quantity increases, the other decreases

All electromagnetic waves travel at a speed of 3.00x10 8 m/s Although waves may travel at the same speed, they may have different wavelengths and frequencies The speed of light, c, is the product of wavelength and frequency C = λν

3. Amplitude The wave’s height from the origin to a crest, or from the origin to a trough

Visible light contains a continuous range of wavelengths and frequencies that separates into a spectrum of colors The visible light spectrum is only a small portion of the complete electromagnetic spectrum Increased Energy

The electromagnetic spectrum encompasses all forms of electromagnetic radiation Each type of radiation has its own wavelength and frequency Energy increases with increasing frequency Increased Energy

II. Particle Nature of Light A. The Quantum Concept Some objects emit certain frequencies of light (radiation) at a given temperature Different colors correspond to different frequencies and wavelengths

Max Planck concluded that matter can gain or lose energy only in small, specific amounts called quanta Planck proposed that objects emit light energy in a quantized, or steplike, manner

This energy of a quantum is related to frequency of emitted radiation by the equation E quantum = hν E quantum = quantum energy H = Planck’s constant = 6.626x J·s ν = frequency of emitted radiation

This explains why energy increases with increasing frequency Increased Energy

B. The photoelectric effect Some metals emit electrons when colored light of a specific frequency shines on them - this is called the photoelectric effect Metals will not eject photoelectrons when the colored light has too low of a frequency

Albert Einstein proposed that electromagnetic radiation has both wavelike and particlelike characteristics - a beam of light can be thought of as a stream of tiny particles, called photons A photon has no mass but carries a quantum of energy

A photon’s energy also depends on its frequency E photon = hν In order for the photoelectric effect to occur a photon must possess, at a minimum, the energy required to free an electron from an atom Photon

III. Atomic Emission Spectra The set of frequencies of the electromagnetic waves emitted by atoms of an element An element’s atomic emission spectrum consists of several individual lines of color, not a continuous range of colors as seen in the visible spectrum

Hydrogen Helium Mercury Uranium

Atoms absorb energy and become excited and release energy by emitting light The fact that only certain colors appear in an element’s atomic emission spectrum means that only certain frequencies of light (or energy) are emitted

IV. Bohr Model of the Atom A. Energy states of hydrogen Niels Bohr studied why hydrogen’s atomic emission spectra is discontinuous When an atom gains energy, it is said to be in an excited state Although hydrogen has only one electron, it is capable of having many different excited states

The lowest allowable energy state of an atom is called its ground state Bohr related these energy states to the motion of the electron within the atom He suggested that electrons move around the nucleus in certain circular orbits Ground State

The smaller the electrons orbit, the lower the atom’s energy state The larger the electrons orbit, the higher the atoms energy state Bohr assigned a quantum number, n, to each orbit The orbits, or energy levels, are not evenly spaced

B. An explanation of hydrogen’s line spectra The hydrogen atom is in the ground state when its electron is in the n=1 orbit When energy is added, the electron “raises” to an excited state and moves to the n=2 orbit At an excited state the electron can drop to a lower-energy state

When an electron transitions to a lower energy-state the atom emits a photon corresponding to the difference between the energy associated with the two orbits ΔE = E higher-energy orbit – E lower-energy orbit ΔE = E photon E photon = hν

Transitions from higher-energy orbits to the second orbit (n=2) account for all of hydrogen’s visible lines - the series of visible lines is called the Balmer series

Transitions from higher-energy orbits to the ground state (n=1) account for hydrogen’s ultraviolet series, or Lyman series

Transitions from higher-energy orbits to the third orbit (n=3) account for hydrogen’s infrared series, or Pashen series

V. The Quantum Mechanical Model of the Atom A. Electrons as waves Louis de Broglie thought that Bohr’s quantized electron orbits had characteristics similar to waves Einstein had proposed waves have particlelike behavior de Broglie thought the opposite to be true that particles, including electrons, have wavelike behavior

From Bohr’s model, de Broglie knew that an electron is restricted to circular orbits of fixed radius For an electron to also have wave-like motion, it is only allowed certain wavelengths, frequencies, and energies

VI. The Heisenberg Uncertainty Principle It is fundamentally impossible to know precisely both the velocity and position of a particle at the same time It is impossible to make any measurement on an object without disturbing it at least a little

A. Hydrogen’s Atomic Orbitals The boundary of an atomic orbital is unclear Chemists arbitrarily draw an orbitals surface to contain 90% of the electron’s total probability distribution

B. The Schrӧdinger wave equation The quantum mechanical model of the atom proposed by Erwin Schrӧdinger is a model in which electrons are treated as waves Applies equally well to atoms of other elements -Bohr’s model only applied to Hydrogen

Limits an electron’s energy to certain values but does not attempt to describe the electron’s path around the nucleus A three-dimensional region around the nucleus called the atomic orbital describes the electron’s probably location

Each orbital, or energy level, contains energy sublevels 1. n = 1 sublevels = s 2. n = 2 sublevels = s and p 3. n = 3 sublevels = s, p, and d 4. n = 4 sublevels = s, p, d, and f

S sublevel - spherical

P sublevel - dumbbell shaped - 3 orbitals of equal energy 2p x, 2p y, and 2p z

D sublevel - 5 orbitals of equal energy d xy, d xz, d yz, d x 2 -y 2, d z 2 4 have identical shapes but different orientations Fifth orbital shaped and oriented differently

F sublevel - 7 orbitals of equal energy Each orbital contains at most 2 electrons

VII. Ground-State Electron Configurations The arrangement of electrons in an atom is called the atom’s electron configuration Most electrons assume the arrangement that gives the atom the lowest possible energy, or the ground-state configuration

A. The aufbau principle States that each electron occupies the lowest energy orbital available The aufbau diagram shows the sequence of atomic orbitals from lowest energy to highest energy

1.All orbitals related to an energy sublevel are of equal energy

2. In a multi-electron atom, the energy sublevels within a principal energy level have different energies

3. In order of increasing energy, the sequence of energy sublevels within a principal energy level is s, p, d, and f

4. Orbitals related to energy sublevels within one principal energy level can have higher energy than orbitals related to energy sublevels within a higher principal level ex. 3d sublevel has more energy than 4s sublevel

B. The Pauli exclusion principle Each electron in an atom has an associated spin Electrons are only able to spin in one of two directions ↑ or ↓ The Pauli exclusion principle states that a maximum of two electrons may occupy a single atomic orbital, but only if the electrons have opposite spins

VIII. Orbital Diagrams and Electron Configuration Notations A. Orbital Diagram A box represents each of the atom’s orbitals Each box is labeled with the principal quantum number and sublevel associated with the orbital ↑↓ PxPx PyPy PzPz

B. Electron Configuration Notation Designates the principal energy level (1,2,3) and energy sublevel (s,p,d,f) A superscript represents the number of electrons in the orbital Carbon: 1s 2 2s 2 2p 2

Noble-gas notation represents electron configurations of noble gases using symbols in brackets Neon: 1s 2 2s 2 2s 6 or [Ne] Noble-gas notation is a short hand for elements with long electron configurations

-The electron configuration for an element can be represented using the noble-gas notation for the noble gas in the previous period and the electron configuration for the energy level being filled Aluminum: 1s 2 2s 2 2p 6 3s 2 3p 1 = [Ne]3s 2 3p 1

C. Sublevel Diagram Produces the sublevel sequence shown in the aufbau diagram

D. Exceptions to predicted configurations The aufbau diagram can be used to write electron configurations only to elements with an atomic number of 23 or less (up to Vanadium)

IX. Valence Electrons Valence electrons are defined as electrons in the atom’s outermost orbitals Group numbers on the periodic table help tell you how many valence electrons are in those elements in that group - Group 1 elements have 1 valence electron - Group 18 elements have 8 valence electrons

A. Electron-dot structures An atom’s electron-dot structure consists of the element’s symbol surrounded by dots representing the atom’s valence electrons Dots representing valence electrons are placed one at a time on the four sides of the symbol and then paired up until all are used Dot structures are important in showing valence electrons because it is these electrons that are available for forming chemical bonds