Chapter 6: The structure of atomsDescribe the evidence for the existence and properties of electrons, protons and neutronsPredict the arrangements of the particles in atomsDescribe isotopes and their compositionCalculate atomic weights from isotopic abundanceDescribe the wave properties of light, and how wave length, frequency, and speed are related

Objectives (continue)Use the particle desription of light, and explain how it is related to the wave descriptionDescribe the four quantum numbers, and give possible combinations of their values for specific atomic orbitalsDescribe the shapes of orbitalsWrite the electron configuration of atomsRelate the electron configuration of an atom to its position in the periodic table

Subatomic particlesElectrons Protons (its mass is almost 1836 times that of the electron)Atoms consist of very small, very dense positively charged nuclei surrounded by clouds of electrons.Open space portion of the atom is from 10,000 to 100,000 times greater than the diameter of the nucleous

ExerciseThe approximate radius of a hydrogen atom is 0.0529 nm, and that of a proton is 1.5 x 10-15 m. Assuming both the hydrogen atom and the proton to be spherical, calculate the fraction of the space in an atom of hydrogen that is occupied by the nucleus. V= 4/3*r3

NeutronsNeutron is an uncharged particle with a mass slightly greater than that of the proton

Nuclide symbolThe composition of a nucleus is indicated by its nuclide symbol.

E: symbol for the elementZ (subscript at the lower left): atomic numberA (superscript at the upper left): mass number

ExampleDetermine the number of protons, neutrons, and electrons in each of the following species?

Mass number and isotopesMost elements consist of atoms of different masses, called isotopes. The isotopes of a given element contain the same number of protons because they are atoms of the same element.Isotopes are atoms of the same element with different masses; they are atoms containing the same number of protons but different numbers of neutrons

Some naturally occurring isotopic abundancesIsotopes10B11B16O17O18O35Cl37Cl234U235U238U% Natural abundance19.9180.0999.7620.0380.20075.77024.2300.00550.72099.2745

BoronOxygenChlorineUranium

The percentages are based on the numbers of naturally occurring atoms of each isotopes.

Many elements occur in nature as mixtures of isotopes. The atomic weight of such an element is the weighted average of the masses of its isotopes. Atomic weights are fractional numbers, not integers.

ExampleCalculation of atomic weightThree isotopes of magnesium occur in nature. Their abundances and masses, determined by mass spectrometry, are listed in the following table. Use this information to calculate atomic weight of magnesiumIsotope24Mg25Mg26Mg% Abundance78.9910.0010.01

ExerciseCalculation of isotopic abundanceThe atomic weight of gallium is 69.72 amu. The masses of the naturally occuring isotopes are 69 amu for 69Ga and 71 for 71Ga. Calculate the percent abundance of each isotope.

The electronic structures of atomAll types of electromagnetic radiation, or radiant energy, can be described in the terminology of wavesThe significant feature of wave motion is its repetitive nature.The wavelength, , is the distance between two adjacent crests.The frequency, , is the number of wave crests passing a given point per unit time

Wavelength and frequency

Light in terms of wave behavior

= speed of propagation of the wave (c)Sunlight contains all wavelengths of visible light, untraviolet (shorter), and infrared (longer) lights.The last two kinds of light cannot be detected by the human eye.

Electromagnetic spectrum

Lights as composed of particles (photons)Each photon of light has a particular amount (a quantum) of energy. Planks equation: E = h or E = hc/ where h is Plancks constant, 6.6260755 x 10-34 J.s

ExampleLight near the middle of ultraviolet region of electromagnetic spectrum has a frequency of 2.73 x 1016 s-1. Yellow light near the middle of the visible region of the spectrum has a frequency of 5.26 x 1014 s-1. Calculate the wavelength that corresponds to each of these two frequencies of light

Exercise Calculate the energy, in joules, of an individual photon of each above mentioned light (ultraviolet and visible lights). Compare these photons by calculating the ratio of their energies.

ExerciseCalculate the frequency of radiation of each of the following wavelengths: 9774 x 10-10m; 442 nm; 4.92 cm; 4.92 x 10-9 cmCalculate the energy, in joules per photon, of the red light, 6573 x 10-10 m,

The wave nature of the electronEinsteins idea that light can exhibit both wave properties and particle propertiesVery small particles, such as electrons, also display wave propertiesLarge objects such as golf balls and moving cars obey the laws of classical mechanics (Issac Newtons laws), but very small particles such as electrons, atoms and molecules do not. A different kind of mechanics, called quantum mechanics (based on wave properties) describes the behavior of very small particles

Basic ideas of quantum mechanics1. Atoms and molecules can exit only in certain energy states. In each enegry state, the atom or molecule has a definite energy. When an tom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition)

Electronic energies of atoms and molecules2.When atoms or molecules emit or absorb radiation (light), they change their energies. The energy change in the atom or molecule is related to the frequency or wavelenght of the light emitted or absorbed:E = h or E = hc/3.The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers.

Quantum numbersAn orbital is a wave function for an electron defined by the three quantum numbers, n, and ml. What the wave function describes, though, is a region in space with a particular shape, where you are likely to find an electron.

In terms of waves, the orbital describes the region in space where the electron density (electron fog) is very thickIn terms of particles, the orbital describes the region in space where there is a high probability of finding the electron

Quantum numbersWe can use quantum numbers to designate the electronic arrangement in all atoms, their so-called electron configurations. Quantum numbers play important roles in describing the energy levels of electrons and the shapes of orbitals that describe distributions of electrons in space.

Principal quantum number, nMain energy levels corresponding to electron shells are designated by a principal quantum number, nBoth the size of orbitals and the magnitude of the average energy of electrons contained therein increase with increasing nPermitted values of n are 1,2,3..., (positive integer) extending through 7 for the known elements

The Azimuthal quantum number, lWithin each main energy level (shell), there are sublevels (subshells). Each sublevel is denoted by an azimuthal quantum number, l. For any shell with a principal quantum number of n, the possible values of l are 0, 1, 2, 3,..., (n-1)Sublevels denoted by different values of l have slightly different energiesl designates different shapes of orbitalsThe italicized letters s, p, d and f correspoding to l values of 0, 1, 2 and 3

The magnetic quantum number, mlAlso n known as orientational quantum numberIt designates the orientation of orbitals in space, and distinguishes orbitals within a sublevel from each otherThe possible values of ml in a subshell with azimuthal quantum number l are given by ml = +l, +(l -1), ..., 0,..., -(l -1), -l

ml designates the specific orbital within a sub-shell.Orbitals within a given subshell differ in their orientation in space, but not in their energies.

s and p electron orbitals

Spin quantum number, msMay have values of only +1/2 or -1/2An electron spins in either two directions and generates a tiny magnetic field with an associated magnetic moment

The values of n, l and ml describe a particular atomic orbital. Each atomic orbital can accommodate no more than two electrons, one with ms = +1/2 and another with ms = -1/2

Example

An electron is in one of the 3p orbitals. What are the possible values of quantum numbers, n, l, ml and ms for the electron

What is wrong with each of the following quantum number designations and/or sublevel names?

Supply the missing quantum numbers and sublevel names.

Exercise 1What is the maximum number of electrons in an atom that have the following quantum numbers? (a) n=2(b) n=3 and l=1; (c) n=3, l=0 and ml=0; (d) n=3, l=1, ml =-1, and ms=-1/2What are the values of n and l for the following subshells? (a) 1s; (b) 3s; (c) 5p; (d) 3d; (e) 4f

Exercise 2Write the subshell notation that correspond to (a) n=3, l=0; (b) n=3, l=1; (c) n=6, l=1; (d) n=3, l=2How many individual orbitals are there in the third shell? Write out n, l and ml quantum numbers for each one, and label each set by the s, p, d, f designation

Atomic orbitalsFor each neutral atom, number of electrons equal to the number of protons in the nucleus (atomic number-Z)Within each atom, these atomic orbitals, taken together, can be represented as a diffuse cloud of electrons

Shapes of atomic orbitalsAn orbital can be drawn as a figure (fuzzy cloud) around the atom nucleus within which there is a high probability (typically 90%) of finding an electron within the orbitalThe two most important aspects of an orbital are its size and shapes orbitals are the only ones that are spherically symmetrical. p orbitals have different orientations in space

d electron orbitals

f electron orbitals

Electron configurationWhich kinds of orbitals contain electrons and the number of eletrons in each kind of orbital of an atom

Ground state electron configurationIsolated atom in its lowest energy, or unexcited state.To describe ground state electron configuration, the guiding idea is that the total energy of atom is as low as possible

Energy level of atomic orbitalsElectrons in atoms occupy the lowest energy level available to themEnergy level diagram that shows the relative energy levels of electrons in various atomic orbitalsDecreasing separation of the energy levels (values of n) with increasing nLevels and sublevels (4s and 3d)

Atom energy level diagram

Placement of electrons in atoms with increasing atomic numberThe placement of electrons is in the order shown in increasing energy levels from bottom to topElectrons are assigned to orbitals in order of increasing value of (n+l)For subshells with the same value (n+l), electrons are assigned first to the subshell with lower n (1 and 2 are Aufbau Principle)

Usual order of filling of atomic orbitals n+l=110123l value234567n+l=2n+l=3n+l=4n+l=5n+l=6n+l=7n+l=8n value

The orbital diagram (orbital notation)Alternative way of expressing electron configurationEach separate orbital is represented by a box or by Individual electrons in the orbitals are shown as arrows pointing up or down to represent opposing spins (ms = +1/2 or 1/2)

Simplified notation

It is expressed by the number and letter representing each kind of orbital and superscript number telling how many electrons are in each sublevel (E.g. 1s1 for H atom)

(notation 1s22s22p3) when in the form of orbital diagram emphasizes that the three electrons are in three available 2p orbitals each occupy separate orbitals (a condition of Hunds rule of maximum multiplicity

Multielectron atom and Quantum numbersEach energy level has at leats one orbitalA single orbital may contain a maximum of only two electronElectrons in atoms are described by 4 quantum numberAn electron in an atom has its own unique set of quantum numbers, no two electrons may have exactly identical numbers (Pauli exclusion principle)

Hunds rule of maximum multiplicityElectrons in a sublevel are distributed to give the maximum number of unpaired electrons1 s2 s2 p

Categories of ElectronsInner (core) electrons are those seen in the previous noble gas. They fill all the lower energy levels of an atom.Outer electrons are those in the highest energy level (highest n value)Valence electrons are those involved in forming compounds. Among the main group elements, the valence electrons are the outer electrons.

n=n=n=n=n=n=n=s1s2d1s2d2s2d3s2d5s1d5s2d6s2d7s2d8s2d10s1d10s2s2p1s2p2s2p3s2p4s2p5s2p6s2

The s,p,d and f blocks of the periodic table

Example

Exercise 4Determine the number of electrons in the outer occupied shell of each of the following elements, and indicate the principal quantum of that shell (a) Na; (b) S; (c) Sr; (e) Ba; (f) Br

Exercise State Pauli Exclusion principle. Would any of the following electron configuration violate this rule: (a) 1s3; (b) 1s22s22px2 Explain?

Schrodinger equation

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