Atomic structure

Light – electromagnetic radiation, can be separated into a spectrum according to wavelength/frequency/energy of components.

Velocity, c = 3.00 x 108 m/s – for all electromagnetic radiation

Frequency – oscillation of electrical field. Cycles per second, hertz, Hz = 1 s-1,

Wavelength, , length of one waveVisible light 700 – 400 nm, 1nm = 10-9 m

c = , short wavelength/high frequency

Orange light, = 620 nm

Ultraviolet (uv) radiation, , 400nmInfrared (ir) radiation, . 700 – 800 nm

Dualistic nature of electromagnetic radiation – shows particle and wave behavior.

Light can be considered streams of particles/discrete energy packets called “photons”Photons – when considered as particlesQuanta – when considered as discrete energy packetsQuanta is energy equivalent of a photon

Quantization of energy – energy can be absorbed or emitted by atomic/subatomic particles only as discrete amounts in atomsAllowed energy (or energy states) are restricted to series of discrete (precisely-defined) energies; electrons in atoms are “quantized” (restricted) to certain discrete energy values.Energy of all moving objects is quantized, but only observed or limiting for atoms/subatomic particles.

Energy of photon, E = h, h = 6.63 x 10-34 J.s [Max Planck, first quantized energy states of excited (heated) atoms in explanation of “Black-body radiation”]

Energy of light determined by inversely by Intensity of light determined by number of photons per unit time.

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Example: blue light, = 470 nm, = 6.14 x 1014 s-1

E = h = (6.63 x 10-34 J. s) x 6.4 x 1014 s-1 = 4.2 x 10-19 J per photon

Example: If lamp emits 25 J energy /s of yellow light, = 580 nm

The Electromagnetic Spectrum

In order of increasing , decreasing , decreasing E:

Cosmic rays < -rays , X-rays < vacuum UV < uv < visible < near IR < far IR < microwave < radio waves

VIS: violet (420 nm), blue, green, yellow, orange, red (700 nm)

H Atomic Spectra:Experimental data led to theory

Emitted energy = “line spectra” = discrete wavelengths- implied quantized energy levels for/in the H atoms

Balmer Equation,

RH – Rydberg constant, RH = 1.097 x 107 m-1

Experimental spectral (lines) series for H:

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Alternate form:

, R = 3.29 x 1015 Hz

Example: Calculate for the third Balmer line.Balmer n1 = 2First line, n2 = 3; 2nd line, n2 = 4; 3rd line, n2 = 5So 3rd Balmer line is electrons transition from n = 5 to n = 2

Bohr Model for H atom

- assumed circular “orbits” for the electron moving around the nucleus;- the principal quantum number, n, n = 1. 2. 3. 4... (ionization), to

distinguish increasing orbit size and energy: n = 1, ground state, lowest energy, electron is normally here; n = 2. 3. 4 … allowed (quantized) excited states for increasing energy. Circular orbits of fixed radius and discrete energies.

- The lone electron is normally in n = 1 orbit (ground state), but can be excited (absorbs energy) into a higher orbit and then emits energy (h) when it relaxes into a lower orbit, E = Ehi – E lo

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- Energy of electron is quantized; electron must be in one of these orbits and each orbit has definite energy: En = -hR/n2

- Treated electron as a particle

Wave Nature of the Electron

de Broglie particle wave (1924):

Photon: E = h = hc/, E = mc2 (Einstein’s mass-energy inter-conversion relation)

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So, for any moving particle/object:

, v = velocity << c (speed of light)

Example:Calculate associate with a baseball (5.0 oz) thrown at speed of 92 miles per hour

M = 5.0 oz x 28.3 g/oz = 142 g

V = 92 mi/h x 1.67 km/mi x 103 m/km x 1h/3600 s = 42.7 m/s

Units: J = N.m, J = (Kg.m.s-2)m = Kg.m2.s-2

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Diffraction of high-speed electrons – Davisson and Germer – 1927-proves wave nature for moving electrons; neutron diffraction.

Schrödnger/quantum mechanical model for H atom

- Start with generalized equation for wave motion, so solution(s) is mathematically correct, but physical interpretation is less certain

- Obtain wave function, n, l, ml (r, , ), as solutions for ground state and all allowed excited states fro H atom

3 variables (coordinates): r – distance from the nucleus; , (angles – shape)

3 quantum numbers: n, l, ml; mathematical indices for orbitals

or 2 are the H atomic orbitals – region in space (volume) in which the electron has greatest probability of existing/being found. “boundary surface” – encloses region of 99.5 % probability for the electron existence. “electron cloud” with varying “electron density” – reflects idea of probability, not certainty.

Shapes of Atomic Orbitals – (see handout)

- shapes determined mainly by dependence on , (angles) and classified according to l, ml quantum number – angular function.

- Energy/size of orbtitals determined by dependence on r and classified according to n quantum number – radial function.

S – orbital – spherical around nucleus, some electron probability at/in the nucleus, greatest probability is at 0.0529 nm, outside nucleus = ao, Bohr radius fro n = 1

P- orbitals – (3), conventionally represented as px, py and pz; as , shape is two tangent spheres with + and – algebraic signs (from sin, cos function) and one nodal (zero) surface/plane where electron has 0 probability of existence/being found.Px along X-axis with yz nodal plane, py along Y - axis with xz nodal plane, pz along Z - axis with xy nodal plane.Equivalent shape (same l) but different orientation in space

d-orbitals – (5) conventionally represented as dxy, dxz, dyz, dx2- y

2, and dz2 ( = d3z

2- r2 = d2z

2-x2-y

2); each orbital has 2 nodal surfaces: dxy has xz, yz nodal planes, dz2

has 2 nodal surfaces between + and – regions.

5 equivalent shapes with different space orientations.

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f- orbitals – 7, complicated shapes; J. Chem. Edu., 41, 354, 358 (1964)

Quantum numbers: n, l, ml

n, principal quantum number; n = 1, 2, 3, ... related to size and energy of orbital; in H the n determines energy of bound electron, En = -hR/n2 (same as Bohr model)

E = 0, for ionized/free electron, so bound electron has negative energy/ lower energy more stable than free electron.

n value defines “shell” of electron levels.

l, azimuthal/orbital angular momentum quantum number; l = 0, 1, 2,... (n-1) maximum; determines shape of atomic orbital: l = 0, s; l = 1, p; l = 2, d; l = 3, f; l = 4, 5, … g, h, …For H atom, orbitals of same n, different l values, have the same energy: E (4s) = E(4p) = E(4d) = E(4f);

For multi-electron atoms, energy depends on n and l quantum numbers. So orbitals have different energy:E(4s) < E(4p) < E(4d) << E (4f)

Notation for atomic orbitals: n, l

n = 1, l = 0 1s orbitaln = 4, l = 3 4f orbitals3p orbitals n = 3, l = 1

Possible valuesNumber of orbitals

n = 1, l = 0, only 1s orbital 1n = 2, l = 0, 1; 2s and 2p orbitals 4n = 3, l = 0, 1, 2; 3s, 3p and 3d orbitals 9n = 4, l = 0, 1, 2, 3; 4s, 4p, 4d and 4s orbitals 16

Orbitals with same l value form/are a subshell; with n = 3 have 3 subshells: 3s, 3p and 3d subshells: “n” number of subshells possible.

ml, magnetic quantum number; ml = l, l-1, … -l; (2l+1) number of possible ml

values; determines number of individual orbitals in a subsehll; related to space orientation of orbitalsl = 0, ml = 0, one s-type orbital.l = 1, ml = +1, 0, -1; three p-type orbitals.

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Note:ml = +1, 0, -1; cannot be assigned directly to px, py, pz.

l= 2, ml = 2, 1, 0, -1, -2; five d orbitals.l = 3, ml = 3, 2, 1, 0, -1, -2, -3; seven f-orbitals.

n determines the “shell”, l determines “subshell” , m l defines orbital.

Calculate number of orbitals in the shell defined by n = 4

n = 4, l = 0, 1, 2, 3; number of ml values possible for each l = 2l +1

1 + 3 + 5 + 7 = 16 orbitlas; i.e. n2 number of orbitals.Not applicable for n ≥ 5, since 5g and 6h orbitals not observed in any known atoms.

Electron Spin

A fourth quantum number is necessary:

a. Experimental: Goudsmit and Uhlenbeck observed doublet lines instead of predicted single lines, indicating 2 closely spaced energy levels instead of one level:

b. Dirac re-calculated Schrodinger equation with correction for relativity and needed an extra quantum number.

Call this spin (magnetic) quantum number., ms = + ½ , - ½ ; “spinning electron is unrealistic”

H – atom: ground state = lowest energy, n = 1, so electron is in 1s orbital (first shell): n = 1, l = 0, ml = 0, ms = + ½ or – ½ .

1st excited state (atom absorbs energy), n = 2 (second shell), so electron can occupy 2s, 2p, (2px, 2py or 2py) orbital (same energy in H) with ms = + ½ or – ½.

2nd excited state, n = 3, electron can occupy 3s, a 3p or a 3d orbital.

3rd excited state, n = 4, electron can occupy 4s, a 4p, 4d or 4f orbital.

Absorbing enough energy allows electron to escape from all nuclear attraction = ionization.

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For absorption of energy, not emission nlo = 1, ground state; nhi = for ionization

E = + 2.18 x 10-18 J per atom

E = (2.18 x 10-18 J/atom)(6.022 x 1023 atoms/mol) = 1.31 x 106 J/mol

1.31 x 103 kJ/mol, experimental ionization energy

Example: If n = 3, l = 1, ml = -1, which orbital? One of the 3p orbitals

Multi – Electron Atoms

Increased nuclear – electron attraction/electron-electron repulsion causes energy differentiation:

1s << 2s < 2p << 3s < 3p << 4s ≤ 3d …

Relative orbital energies – when these orbitals are being filled:

1s < 2s < 2p < 3s < 3p < 4s < 3d 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p

This order true as valence electrons are filling these orbitals, however, after being filled3d < 4s, 4d < 5s, 4f < 5d < 6s, 5f < 6d < 7s

Aufbau/Build-up Principle for Electron Configurations

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How electrons occupy orbitals lowest energy filled first.Consequence of Pauli Exclusion Principle: no two electrons in same atom can have identical sets of the 4 quantum numbers;

Maximum of 2 spin-paired electrons can occupy same orbital.

ms = + ½ , ms = - ½ ; notation

Electron Configurations:

H 1s1, one electron in 1s orbital

2He - 1s2 1s, closed shell configuration

3Li

a, b - same energy, lowest energy, ground state, parallel spin

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c, d - allowed excited (higher –energy) states

e - forbidden state (impossible, violates Pauli Exclusion Principle)

Hund’s rule –degenerate (same –energy) orbitals fill with maximum number of parallel electron spins; electron spin pairing requires energy.

6C 1s2 2s2 2px1 2py

1 7N – 1s2 2s2 2px1 2py

1 2pz1

8O – 1s2 2s2 2px2 2py

1 2pz1

10Ne – 1s2 2s2 2p6 closed shell configuration

Useful abbreviation = [rare gas] closed-shell electrons:

3Li - 1s2 2s1 or [He] 2s1 emphasizing valence electrons:

11Na – 1s2 2s2 2p6 3s1 or [Ne] 3s1

Emphasize similar chemistry of elements in same family:

19K – 1s2 2s2 2p6 3s2 3p6 4s1 or [Ar] 4s1

Electronic Structure of Periodic Table

1 H He2 2s 2p Ne3 3s 3p Ar4 4s 3d 4p Kr5 5s 4d 5p Xe6 6s 4f 5d 6p Rn7 7s 5f 6d 7p

S - block f- block d – block p - block

s and p blocks – main group elements

d – block – transition metals

4f – lanthanides, rare earths5f – actinides

Stresses valence electrons/orbitals being added/filled

Vertical column of PT = chemical family, similar chemistry

Horizontal row of PT = periods; n = 1, H – He; n = 2, Li – Ne etc

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21Sc [Ar] 4s2 3d1 transition metals

Predict 4s ≤ 3d, so 4s ≈ 3d energySc: [Ar] 4s2 3d1 but Zn: [Ar] 3d10 4s2

So, Sc – Zr - [Ar] 4s2 3dn or [Ar] 3dn 4s2

- orbitals written in order of increasing energy- exceptional stability of nd5 and nd10; hall-filled and completely filled d-

subshells

24Cr, expect [Ar]4s2 3d4, observe [Ar] 4s1 3d5

Exists as excited state ground state (lowest energy)

29Cu, expect [Ar] 4s2 3d9, observe [Ar] 4s1 3d10

After filling, (n-1)d subshell always lower than ns subshell:

32Ge: [Ar] 3d10 4s2 4p2, four valence electrons: 4p2, 4s2; Ge2+, Ge4+

4 th Period: first long period, 4s, 3d, 4p 2 + 10 + 6 = 18 electrons

5 th Period: 5s ≤ 4d < 5p [Kr] 5s2 4dn

Or [Kr} 4dn 5s2 (more exceptions)

6 th Period: 6s ≤ 4f ≤ 5d < 6p 32 electrons

57La – 70Yb more or less [Xe] 6s2 4fn, some exceptions

71Lu – 80Hg [Xe]4f1 46s2 5dn or [Xe} 4f14 5dn 6s2

81Tl – 86Rn must be [Xe] 4f14 5d10 6s2 6p1-6

7 th Period: 7s ≤ 5f ≤ 6d < 7p

89Ac – 102No - more or less [Rn]7s2 5f1-14

103Lr – 109 Mt - [Rn] 5f14 7s2 6d1-x

Practice Electronic Configurations

Closed – shell configurations: 2He, 10Ne, 18Ar, 36Kr, 54Xe, 86Rn

1. 16S – [Ne] 3s2 3p4

2. 26Fe – [Ar] 4s2 3d6 or [Ar] 3d6 4s2

3. 51Sb – [Kr] 5s2 4d10 5p3 [Kr] 4d10 5s2 5p3

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4. 60Nd - [Xe] 6s2 4f4

(More practice with Heavy atoms...)

Electronic Configurations for heavy atoms - use PT

82Pb - [Xe] 6s2 4f14 5d10 6p2 [Xe] 4f14 5d10 6s2 6p2

77Ir – [Xe] 6s2 4f14 5d7 [Xe] 4f14 6s2 5d7 or [Xe] 4f14 5d7 6s2

93Np [Rn] 7s2 5f5

47Ag – [Kr] 5s2 4d9 [Kr] 5s1 4d10 or [Kr] 4d10 5s1

Electron Configuration of Ions

Cations – atoms have lost electronsAnions – atoms have gained electrons

Cations:Remove highest energy valence electrons first.

49In+, In3+; atom [Kr] 4d10 5s2 5p1

In+ [Kr] 4d10 5s2 In3+ [Kr] 4d10

- careful with transition metal cations; Never retain any ns valence electrons in the cation:

27Co [Ar] 4s2 3d7 or [Ar] 3d7 4s2

Co2+ [Ar] 3d7, Co3+ [Ar] 3d6, Co+ [Ar] 3d8

Anions:Add electrons to (usually) complete closed-shell:

Oxide, O – 1s2 2s2 2p4 + 2e 1s2 2s2 2p6 = [Ne], O2

Phosphide, P – [Ne] 3s2 3p3 + 3 e [Ne] 3s2 3p6 = [Ar], P3

Periodic Behavior of Atomic Properties

Atomic radii – distance between nucleiAssume atoms are tangent spheres in solid state

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In Cu(s) measure Cu-Cu distance as 256 pmr(Cu) – 256/2 128 pm (I pm = 10-12 m)

r increases down families (group) in creasing n value of valence electrons – so increasing size of orbitals/atoms;

r decreases left to right (period) increasing effective nuclear charge Z*, as increasing electrons fail to completely shield increasing number of protons in nucleus.

Ionic radii – radii of ions – sum of anion and cation radii = internuclear distance

Internuclear distance = ranion + rcations

MgO – internuclear distance = 205 pm

Mesure r (O2-) = 140 pm; r (Mg2+) = 205 – 140 = 65 pm

Cations – smaller than parent atoms – fewer electrons, same Z, and lose valence electrons(s) from largest orbital.

Relatively large decrease in size: Li 157 pm, Li+ 58 pm, Be 112 pm, Be2+ 27 pm;B 88 pm, B3+ 12 pm (too small to exist; so covalent)

Ions – relative sizes – parallel trends of parent atoms

Anions – larger than parent atoms; more electrons but same Z. O 66 pm O2- 140 pm; F 64 pm, F 133 pm

Isoelectronic – species with same number of electrons

N3-, O2-, F-, Ne, Na+, Mg2+, Al3+ (isoelectronic)

171 pm --- decreasing radii – 53 pm

Relative size: Mg2+ < Ca2+, O2-> F-

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Ionizatino Energy

Cu(g) Cu+(g) + e(g), I1 = 745.1 kJ/molFirst ionization energy – in gas phase

Cu+(g) Cu2+(g) + e(g), I2 = 1955 kJ/mol

Second ionization energy, always I2 > I1

- usually decrease down family because larger n gives larger atoms- usually increase left to right because increasing Z*, but many small

irregularities

Lowest I1, group 1, Li > Na > K > Rb > Cs ; [ ] ns1 – easy to ionize

Highest I1, group 18, He > Ne > Ar > Kr > Xe > Rn; closed- shell configuration = most stable = hardest to ionize.

Generally I1 < I2 < I3… removing electron from cation

I2 >> I1 for group 1I3 >> I2 > I1 for group 2Valence electrons are easier to ionize than closed-shell configuration

Group 1 [ ] ns1, group 2 [ ] ns2

Metallic Character – lower left PT, Cs most metallic with lowest ionization energy. Metal solid has cations in fixed position with a “sea of valence electrons” – so conduct electricity so easily: Cu: Cu+ and mobile electrons.

Non-metals – upper right PT; highest ionization energies

Metalloids – semi metals: Si, Ge, As, Sb, Te, Po

Electron Affinity – Eea or EA1, EA2, energy exchanged (released, +ve; absorbed/needed, -ve) when electron added to gaseous atom/anion:

+ve value – energy released (favorable)-ve value – energy absorbed (unfavorable)

Periodic Behavior less regular/obvious for Eea values, but: Rare gases have large –ve Eea values – unfavorableHalogens (group 17) have large +ve values = favorable

Second Eea (EA2) always –ve, unfavorable in gas phase

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EA2 or oxygen is much less –ve than EA2 of fluorine, so O2- possible in formation of compounds, but F2- never seen.

General Chemical Trends in PT

s- block elements – group 1 – alkali metals, [ ] ns1, M+ cations only

group 2- alkaline earth metals, [ ] ns2, M2+ cations; reactive metals, low I1; most metallic = Cs, Ba; least reactive Be

p- block elements – groups 13 – 18 [ ] ns2np1-6 ; metals, lower left; metalloids diagonal; non-metals – upper right, high I1, +ve Eea (except group 18), gain electrons to form anions; metals lose electrons for cations.

d-block elements – group 3 – 12, transition metals, multiple oxidation state cations: Cu2+, Cu+, Cu3+; Co2+, Co3+, Co+;

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