Chapter 5. Periodicity And The Periodic Table

Chapter 5.Periodicity and the Periodic Table

Chapter 5.Periodicity and the Periodic TableMany properties of the elements follow a regular pattern.In this chapter, we will look at theory that has been developedto explain this periodicity

ionizationenergy: theamount ofenergy needed toremove anelectron

Much of what we have learned about atomic and molecular structure, hascome from our understanding of how matter interacts with light.What is light?The interaction of light with matter forms the foundation of ourunderstanding of atomic structure, molecular structure, and the structureof the universe!

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Light: What is it?Light is referred to as electromagnetic radiationLight has both wave properties and particle propertiesAll light, whether radiowaves or visible light, travels as the same speed, 3 *108 meters/secAs a result, since the length of each wave decreases from left to right, the frequency of thepeaks an troughs of the waves shown above must increase from left to rightReferring to light as a particle, known as a photon of light, the energy of each particle oflight is also known to increase from left to rightThe total energy of course depends on the frequency of the light and the number of particles

Light also has a magnetic field associated with. If varies in the same fashion asthe electric field, traveling at the same speed but perpendicular to the electricfield. Both the electric and magnetic fields are used in medicine and scienceA MRI (magnetic resonance image ) of aheart and lungs using radiowavefrequencies in the presence of a strongexternal magnetic field

The interaction of light with matter forms the foundation of ourunderstanding of molecular structure. How so?Wave properties of lightc λν where c 3x1010 cm/s speed of light in a vacuumλ wavelength of light and ν frequency of lightParticle properties of lightE hν where E is the energy of a photon of light andh 6.626 x 10-34 J.sThe total energy associated with light depends on the frequency and alsothe intensity (the number of photons per unit time)

Heisenberg uncertainty principle:(uncertainty in position)(uncertainty in momentum (mv)) h/4π

How does the emission spectrum of black body look like?

White light that passes through a prismis separated into all colors that together arecalled a continuous spectrum gives thecolors of a rainbowWhen an element is heated, it gives offlight. However the entire rainbow ofcolors is absent and only certain colors arepresent. Each element gives it ownspectrum of color. Not all of the light is inthe visible region. Depending on thetemperature, the element, some lightcovering a large portion of theelectromagnetic spectrum can be observed

What happens if we take a hydrogen atom and heat it up, or forthat matter, any element?

The emission spectrum of H and sodium atoms in the visible region ofthe spectrumThe significance of observing discrete line may not be immediatelyapparent but these atomic species when heated do not give off allwavelengths of light but only discrete wavelengths

The interpretation of these observations is that upon heating H atoms, thehydrogen does not emit any light until a certain amount of energy is putinto the atom. Since an atom of hydrogen consists of only a proton andan electron, it is believed that the emission of light by the hydrogen isdue to excitation of the electron.Excited hydrogenenergyUnexcited hydrogen

The interpretation of these observations is that upon heating H atoms, thehydrogen does not emit any light until a certain amount of energy is putinto the atom. Since an atom of hydrogen consists of only a proton andan electron, it is believed that the emission of light by the hydrogen isdue to excitation of the electron. Alternatively, we can’t excite hydrogenelectronically unless we put in the correct amount of energy.Excited hydrogenenergyhν given offE hνUnexcited hydrogen

Balmer equation1/ λ R[1/22-1/n2] whereR 1.097x10-2 nm-1 and n is some integer 2The energy of the light observed in the visibleregion is only a portion of the light emitted by ahydrogen atom. This transition occurs in theultraviolet region

A model has been devised to explain this phenomenaThink of the model as a bookcase with eachsucceeding shelf getting closer and closerDepending on the element, different electronictransitions can be observed. The emphasis her iselectronic, the electrons are being excited todifferent levelsAn e-

hydrogenionizationpotentialI.E.

Balmer Rydberg equation1/ λ R[1/m2-1/n2] where R 1.097x10-2 nm-1 andn is some integer m. This equation accounts forthe lines observed for hydrogen both in the visibleregion and elsewhere.Why are these other lines also included?

Why are the orbital energies of hydrogen written as 1s, 2s,2p, 3s, 3p, 3d .?Also why the difference in energy between the 2s and 2plevel, for example, in a multi-electron atom?Many more emission lines are observed in multi electronatoms. These terms are used to describes the levels anelectron can occupy

States needed to explain emission lines in:multi-electron states in a magnetic fieldmulti-electron atom3d3d3p3p3s3sEnergy2p2p2s2s1s1sAbsorption lines wereobserved to increase inmagnetic field

What is observed in the spectra of multielectron atoms aremultiple lines closely spaced followed by big gaps.The number of lines observed with other atoms are numerous andbeyond our concern. We will be interested in summarizing thetheory that has been developed to explain these emision lines.

Attempts to explain the emission (and absorption spectra) of atomichydrogen and the other atoms, resulted in discovery/development of amathematical equation with properties that mimicked the observedspectra of atoms.Schroedinger Equation is a differential equation:Properties of a differential equation:1.the equation may have more than one solution.2.any combination of solutions (sum or difference) is also asolutionSolutions to this equation are found only when certain terms in theequation have unique values: these terms have been called quantumnumbers and have been given the symbols: n, l, m, and s.

The quantum numbers have names and also must have certainrelationships between each other, otherwise the equation vanishes (hasno solution)n principle quantum number, must have integer values of 1, 2, 3, L is called the angular momentum quantum number and must haveinteger values from –(n-1), -(n-2), 0m is called the magnetic quantum number and can have values from–L, (L-1),.0,. L (cap L used here because lowercase l looks like the number 1)s is called the spin quantum number, must be 1/2 or –1/2Each electron in an atom is assigned 4 quantum numbers; no twoelectrons can have the same 4 quantum numbers or the solutionvanishes?

What do the solutions to the Schroedinger Equation look like and whatinformation do they provide.The solutions are mathematical equations often described in sphericalcoordinates.What are spherical coordinates?What are Cartesian coordinates?

Cartesian Coordinatesz. (x1,y1,z1)yx

Spherical Coordinatesz. (r,θ,ϕ)yϕθx

Some solutions to the Schroedinger EquationSolution to this equation are called Ψ (psi)What do they look like:Ψ1s (1/πa3)(2.718)r/a where a is a constant 5.29*10-9 cm and r is thedistance of the particle from the origin(n 1, l 0)Ψ2s 1/4(1/2πa3).5(2-r/a)(2.718)r/2a(n 2, l 0)Ψ2p 1/4(1/2πa3).5(r/a)(2.718)r/2acos θ(n 2, l 1) What is the physical interpretation of the information they provide?The functions Ψ (psi) are amplitude functions, when squared andmultiplied by an element of volume, they provide the probability offinding an electron at some location ((r,θ,ϕ or x,y,z) in space.What do these functions look like?

1s2sn 1, l 03sn 2, l 0n 3, l 0 Ψ1sa node is aΨ2s region where thefunction 0Ψ3s

What do the p orbitals look like?How do they compare in energy to s orbitals?

P orbitalsn 2, l 1, m -1- n 2, l 1, m 0 -n 2, l 1, m 1 Ψ2p

What do the d orbitals look like and howmany are there?How do they compare in energy to p orbitals?

Ψ3dΨ4f

Why are these orbitals significant:These orbitals are solutions to the Schroedinger Equation for thehydrogen atom. However they are very useful because they provide amodel to mimic the behavior observed for the remaining elements inthe periodic table.Rules for predicting the electronic properties of the remaining elementsof the periodic table:1. Electrons want to occupy orbitals with the lowest energy possible2. No two electrons can have the same four quantum numbers3. Electrons repel each other and prefer to go in orbitals of equal energythat are unoccupied; they prefer to go in with the same spin (Hund’srule)4. A maximum of 2 electron are possible in any given orbital

H 1 proton and 1 electronDesignation: 1s1

Remember, if we excite hydrogen, we can excite it to a 2s level,3s level, 4s level, and then it can decay from any one of theseleves to a lower level by emitting a specific wavelength of light.This model explains the observed spectra of hydrogen, bothemission (light given off from an exited state to one of lowerenergy) or absorption (light absorbed in going from the groundstate to an excited state)

He has 2 protons and 2 electrons; note that theorbital energy scale will change because eachelectron will be attracted to a nucleus that has 2protonsDesignation: 1s2Also note that this fills the 1s level; the nextlevel is much higher in energy

Li has 3 protons and 3 electrons; note that theorbital energy scale will change again becauseeach electron will be attracted to a nucleus thathas 3 protonsDesignation: 1s2 2s1

Be has 4 protons and 4 electrons; note that theorbital energy scale will change because eachelectron will be attracted to a nucleus that has 4protonsDesignation: 1s2 2s2

B has 5 protons and 5 electrons; note that theorbital energy scale will change because eachelectron will be attracted to a nucleus that has 5protonsDesignation: 1s2 2s2 2p1

C has 6 protons and 6 electrons; note that theorbital energy scale will change because eachelectron will be attracted to a nucleus that has 6protonsDesignation: 1s2 2s2 2p2Note Hund’s rule: electrons occupy differentorbitals with the same spin

N 7 has protons and 7 electrons; note that theorbital energy scale will change because eachelectron will be attracted to a nucleus that has 7protonsDesignation: 1s2 2s2 2p3

O has 8 protons and 8 electrons; note that theorbital energy scale will change because eachelectron will be attracted to a nucleus that has 8protonsDesignation: 1s2 2s2 2p4

F has 9 protons and 9 electrons; note that theorbital energy scale will change because eachelectron will be attracted to a nucleus that has 9protonsDesignation: 1s2 2s2 2p5

Ne has 10 protons and 10 electrons; note that theorbital energy scale will change because eachelectron will be attracted to a nucleus that has 9protonsDesignation: 1s2 2s2 2p6Also note that this fills this level

Na has 11 protons and 11 electrons; note that theorbital energy scale will change because eachelectron will be attracted to a nucleus that has 11protonsDesignation: 1s2 2s2 2p6 3s1

Name the element with the following electronic configurations1s2 2s2 2p6 3s1(Ne 3s1)Na1s2 2s2 2p6 3s2Mg1s2 2s2 2p6 3s2 3p6Ar1s2 2s2 2p6 3s2 3p6 4s1K1s2 2s2 2p6 3s2 3p6 4s23d5Mn1s2 2s2 2p6 3s2 3p6 4s2 3d103p3As

In a multi-electron atom, which orbital shape do you think best shieldsthe nucleus to an electron further out in space (in a higher level)?s orbitalp orbitald orbitalf orbital

Some anomalous electron configurationsStability associated with half filled and fully filled shellsCr [Ar] 4s2 3d4 [Ar]4s1 3d5Cu [Ar] 4s2 3d9 [Ar]4s1 3d10

Which of the following combination of quantum numbers canrefer to any electron in a ground state Co atom (Z 27)?1.n 3, l 0, ml 22.n 4, l 2 ml -23.n 3, l 1, ml 0What type of electron has the following quantum numbers?n 3, l 03s orbital,n 4, l 2a 4d orbital, ml -2, -1, 0, 1, 2n 3, l 1a 3p orbital, ml -1, 0 ,1