Mark S. Cracolice Edward I. Peters Mark S. Cracolice The University of Montana Chapter 11 Atomic Theory: The Quantum Model of the Atom

Dual Characteristics of Light Light has both wavelike properties and particle- like properties. In one hand, light can be considered as an electromagnetic radiation characterized by its velocity c (velocity in vacuum is x 10 8 m/s ) its wavelength λ (lambda) or its frequency ν (nu) Wavelength of blue light is 470 nm Wavelength of red light is 700 nm c = λ. ν Long-wavelength has lower frequency than short-wavelength

Dual Characteristics of Light On the other hand, light can be considered as a stream of “particles” called photon, with energy given by E = h ν h is the Planck constant. Photons of blue light (higher frequency) are more energetic than red light (lower frequency).

Continuous Spectrum When white light is passed through a prism, it produces a spectrum which contains all wavelengths. A spectrum that contains all the wavelengths is called continuous spectrum.

Continuous Spectrum

Line Spectrum of Hydrogen When light emitted by hydrogen atoms is passed through a prism, we see only a few lines, each of which corresponds to discrete wavelength. The hydrogen spectrum is called a line spectrum.

Light Emitted by Hydrogen Atoms

Line Spectrum of Hydrogen The line spectrum of hydrogen indicates that only certain energies are allowed for the electron in the hydrogen atom.

Light Emitted by Atoms

Bohr Model of Hydrogen Atom In 1913 Niels Bohr proposed that the electron in a hydrogen atom moves around the nucleus only on certain allowed orbits and thus the energy of the electron in the hydrogen atom is quantized (electron energy can only have discrete set of values)

Bohr Model of Hydrogen Atom

When an electron jumps from an excited state to a lower energy state, it releases the energy by emitting a photon of electromagnetic radiation. The energy of this photon is quantized, and thus corresponds to a line in the spectrum of the element.

Bohr Model of Hydrogen Atom

Quantum Mechanical Model In 1927 Werner Heisenberg derived the uncertainty principle, which states that it is impossible to know simultaneously both the momentum (mv ) and the position of a particle with certainty. Therefore we cannot speak of the orbit of an electron around the nucleus

Quantum Mechanical Model In 1926, Ervin Schrodinger advanced the famous wave equation Hψ = E ψ E is the energy of the atom, and ψ(x,y,z) is called the wave function. The wave function ψ that describes the state of one electron is called orbital.

Quantum Mechanical Model The square of the orbital │ψ(x,y,z)│ 2 is a direct measure of the probability density of finding the electron in that orbital at any particular point. The region of space in which an electron is most likely to be found can be visualized as the orbital itself.

Three orbital quantum numbers Atomic orbital are specified by three orbital quantum numbers: a) The principal quantum number n. n has integral values 1, 2, Orbitals with the same quantum number n are said to belong to the same shell. Each shell has n 2 orbitals As n increases, the orbital becomes larger and the electron spends more time further from the nucleus and the electron is less tightly bound to the nucleus.

Quantum Mechanical Model

Quantum number specification of orbital b) The orbital shape quantum number l (also called the angular momentum quantum number). For each value of n, l can have n integral values from 0 to n-1. Orbital with l = 0 is called orbital s Orbital with l = 1 is called orbital p Orbital with l = 2 is called orbital d Orbital with l = 3 is called orbital f Orbitals with the same quantum numbers n and l are said to belong to the same subshell

Quantum number specification of orbital c) orbital orientation quantum number m l For a given value of l, m l can have (2l+1) integral values between l and -l, including zero There are 2l+1 orbitals in each subshell Thus we have l = 0, one orbital ns l = 1, three orbitals np l = 2, five orbitals nd l = 3, seven orbital nf.

Orbital Shapes

Electron spin quantum number Spectral data indicate that electron has a magnetic moment with two possible orientations relative to an external magnetic field. Electron spin quantum number m s has been introduced to describe the two spin states of the electron. (m s can have only one of two values +1/2 and -1/2) The state of the electron is thus specified by four quantum numbers : n, l, m l and m s.

THE PAULI PRINCIPLE In an atom no two electrons can have the same set of four quantum number. Since electrons in the same orbital have the same values of n, l, m l they must have different values of m s. Thus an orbital can only hold two electrons with opposite spin (two different values of m s )

THE PAULI PRINCIPLE An orbital can only hold two electrons. Therefore the maximum number of electrons in a sublevel l is twice the number of orbitals in the sublevel, 2 (2l+1). The maximum number of electrons on level n is 2 n 2

ORBITAL ENERGY Orbital energy depends on quantum numbers n and l. Energy levels with the same principal quantum number n are said to belong to a same principal level. Energy increases with increasing n. For each principal level there are one or more sublevels, which are ns, np, nd, nf... In general the energy order is ns< np < nd < nf

ORBITAL ENERGY

Electron Configuration Electron Configuration: A list of the number of electrons in each energy level in an atom. Two principles are used 1.At ground state the electrons fill the lowest-energy orbitals available. 2. No orbital can have more than two electrons.

Electron Configuration The number of electrons at any sublevel is shown by a superscript number.

Electron Configuration. Block Elements

Electron Configuration Example: Write the electron configuration of aluminum. Solution: First, locate Al in the periodic table. It is Group 3A and Period 3, the first element in the 3p block. Now write the electron configuration of its highest occupied energy sublevel: 3p 1 (continued on the next slide)

Electron Configuration 3p 1 To the left of what is written, we next list all lower-energy sublevels in order of increasing energy. 1s 2s 2p 3s 3p 1 Now write the number of electrons that fill each sublevel. 1s 2 2s 2 2p 6 3s 2 3p 1 Finally, check for the correct number of electrons: = 13 = Z for Al

Electron Configuration Let’s compare the electron configuration of Al with the electron configuration of Ne: Al: 1s 2 2s 2 2p 6 3s 2 3p 1 Ne: 1s 2 2s 2 2p 6 Note that they are the same through the first 10 electrons, which are the n = 1 and n = 2 electrons.

Electron Configuration The Al configuration contains a Ne core: Al: 1s 2 2s 2 2p 6 3s 2 3p 1 Since the n = 1 and n = 2 electrons are in the inner part of the atom and therefore not involved in bonding, we don’t need much detail about their configurations.

Electron Configuration A noble-gas core is commonly used in writing electron configurations Al:1s 2 2s 2 2p 6 3s 2 3p 1 Al: [Ne]3s 2 3p 1

Electron Configuration To Write an Electron Configuration Using a Noble-Gas Core: 1. Find the noble gas (Group 8A/18 element) with the highest atomic number that is less than the atomic number of the element for which the electron configuration is being written (last element of previous period). 2. Write the elemental symbol of the noble gas in square brackets. 3. Write the remainder of the electron configuration using the previously-described procedure.

Electron Configuration Exceptions There are two exceptions to the filling order of 4s and 3d 1. Chromium (Z = 24) Instead of [Ar]4s 2 3d 4 More stability if five d orbitals are half-filled. Electron configuration of chromium [Ar]4s 1 3d 5.

Electron Configuration Exceptions 2. Copper (Z = 29) Systematic prediction: [Ar]4s 2 3d 9 There is a special stability when all five d orbitals are filled. Electron configuration of copper: [Ar]4s 1 3d 10

Valence Electrons Valence Electrons: The s and p electrons of the highest- occupied energy level; the outermost electrons of an atom. Lewis Symbol:Element symbol surrounded by dots that represent the valence electrons of an atom of that element.

The Atomic Radii General Trends in Atomic Radii

First Ionization Energy First Ionization Energy: The energy required to remove one electron from a neutral gaseous atom of an element. Mg kJ  Mg + + e

The Periodic Table: groups and series

The Periodic Table: Metals, nonmetals and metalloides

Trends in the Periodic Table

General Trends in Metallic Character

Homework Homework : 21, 31, 39, 43, 45, 47, 49, 57