# The Wave Nature of Light. Waves To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. The distance.

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The Wave Nature of Light

Waves To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. The distance between corresponding points on adjacent waves is the wavelength ( ).

Waves The number of waves passing a given point per unit of time is the frequency ( ). For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

Electromagnetic Radiation All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  10 8 m/s. Therefore, c =

The Nature of Energy The wave nature of light does not explain how an object can glow when its temperature increases. Max Planck explained it by assuming that energy comes in packets called quanta.

The Nature of Energy Einstein used this assumption to explain the photoelectric effect. He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.63  10 −34 J-s.

The Nature of Energy Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c = E = h

The Nature of Energy Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.

The Nature of Energy One does not observe a continuous spectrum, as one gets from a white light source. Only a line spectrum of discrete wavelengths is observed.

The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 1.Electrons in an atom can only occupy certain orbits (corresponding to certain energies).

The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 2.Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 3.Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = h

The Nature of Energy The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:  E = −R H ( ) 1nf21nf2 1ni21ni2 - where R H is the Rydberg constant, 2.18  10 −18 J, and n i and n f are the initial and final energy levels of the electron.

The Wave Nature of Matter Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties. He demonstrated that the relationship between mass and wavelength was = h mv

Atomic Electron Configurations

Electron spin 1.Quantum number (m s ) – electron spin magnetic quantum number 2.To totally understand this, we must first learn about magnetism.

Paramagnetism and Unpaired Electrons Substances are: Diamagnetic if they are repelled by a strong magnet Paramagnetic if they are attracted by a magnet

Electron spins 1.Paramagnetism arises from electron spins. 2.Electron spins have 2 orientations 3.Therefore, the electron spin is quantized and can have a quantum number 4.Possible values: m s = + ½ or – ½

Paramagnetism and diamagnetism Paramagnetism occurs in substances in which the ions or atoms have unpaired electrons Diamagnetism occurs in substances in which the ions or atoms have paired electrons

Pauli Exclusion Principle No two electrons in an atom can have the same set of four quantum numbers. No atomic orbital can contain more than two electrons.

What are the possible numbers of electrons in…. The s orbitals: 2 The p orbitals: 6 The d orbitals: 10 The f orbitals: 14

Aufbau Principle Electrons are placed in the lowest energetically available subshell. An orbital can hold at most 2 electrons. If two or more energetically equivalent orbitals are available (e.g., p, d etc.) then electrons should be spread out before they are paired up (Hund's rule).

Atomic energy diagram

Which of the subshells should be filled first?

Order of orbital filling

Types of Notations and Valence Electrons 3 types: Electron Configuration Na: Noble gas notations Na: Orbital notations

Exceptions to the Rule Cr Cu

Electron configurations of ions (excited state) Rules: Remove electrons from the electron shell of the highest n If there is a choice of a subshell within the nth subshell, the electron electrons are removed from the maximum l.

E - Configurations of Ions Tin Tin 2+ Tin 4+

Quantum Mechanical Model of the Atom

Erwin Schrödinger Professor of physics! Wrote daring equations! Confounded his critics!

The quantum mechanical atom It is impossible to specify the precise position of an electron in an atom at a given instant – Heisenberg Uncertainty Principle

Quantum Numbers Every electron in an atom has a set of four quantum numbers. Pauli Exclusion Principle – No two electrons in an atom can have the same set of four quantum numbers.

First Quantum Number (n) Principle energy level n = 1, 2, 3, 4, etc. As n increases, the electron is farther out from the nucleus.

Second quantum number ( l ) Each principal energy level includes one or more sublevels. l = the shape of the orbital (s, p, d, f) l : 0 to n-1 Quantum number l Type of sublevel 0s 1p 2d 3f

Third quantum number m l Each sublevel contains one or more orbitals. m l determines the direction in space of the electron cloud surrounding the nucleus (orientation of the orbital). - l to l

m l = -1m l = 0m l = 1 m l = -2m l = -1m l = 0m l = 1m l = 2 7.6

Fourth quantum number m s Associated with electron spin. An electron has magnetic properties that correspond to those of a charged particle spinning on its axis. m s = + 1/2 or -1/2

Ex For principal quantum level n=5, determine the number of allowed subshells, and give the designation of each.

Ex Which of the following sets of quantum numbers are not allowed in the hydrogen atom? a. n=2, l =1, m l = -1 b. n=1, l =1, m l = 0 c. n=8, l =7, m l = -6 d. n=1, l =0, m l = 2

Ex Give a possible set of values of the four quantum numbers for all the electrons in a Boron atom

Ex Give a possible set of values of the four quantum numbers for all the electrons in a nitrogen atom if each is in the ground state

Ex Which of the following electron configurations correspond to an excited state? Identify the atoms and write the ground state electron configuration where appropriate. a. 1s 2 2s 2 3p 1 b. 1s 2 2s 2 2p 6 c. 1s 2 2s 2 2p 4 3s 1 d. [Ar]4s 2 3d 5 4p 1

E- Configuration Battleship s-sublevel – Destroyer – p-sublevel – Cruiser – d-sublevel – Battleship –

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