Atomic Structures Period Properties Electromagnetic Radiation and Radiation

Atomic Structures & Period Properties • • Electromagnetic Radiation and Radiation Energy Photoelectric Effect and Its Frequency Dependence Atomic Spectrum of Hydrogen Gas The Bohr’s Model of H-atom Quantum Mechanic Model for Electrons in Atoms Atomic Orbitals and Quantum Numbers Electron Spin and Pauli Exclusion Principle Electron Configurations for Atoms with many Electrons • Periodic Trends and Atomic Properties

Various Depictions of the “Plum Pudding Model”

Thomson’s Atomic Model* (1904) sphere of uniform positive charge negatively charged “corpuscle” Equal angular intervals d ~ “atomic dimensions” * Joseph J. Thomson, “On the Structure of the Atom” Philosophical Magazine and Journal of Science, Series 6, Vol. 7, No. 39, pp. 237 -265

Atomic Modeling in the Early 20 th Century: 1904 -1913 Charles Baily University of Colorado, Boulder Oct 12, 2008

Key Themes to Atomic Modeling Stability of the atom Dynamics of its parts Chemical/spectral properties

Spectrum of White Light

Electromagnetic Spectrum

Electromagnetic Radiation • Electromagnetic Radiation = Light: 1. radiation energy that propagates through space in wave form 2. The speed of light is constant in a given medium 3. The speed of light through space is c = 2. 998 x 108 m/s 4. 5. c = ln (where l = wavelength, n = frequency) Light with longer wavelength has lower frequency, and one with higher frequency has shorter wavelength. 6. According to Quantum Theory: Radiation Energy depends only on frequency: En = hn 7. where the Planck constant and h = 6. 626 x 10 -34 J. s

Electromagnetic Radiation

Photoelectric Effect • Photoelectric current

Photoelectric Effect • When light with energy greater than the minimum value strikes a metal plate (the cathode), electrons are ejected • A potential gradient is created and electrons flow in the circuit and photoelectric current is produced. • Different metals require different minimum energy to produce photoelectric effect. This is called the work function. • If light with energy lower than the minimum value is used, no photoelectric effect is produced. • The minimum energy needed to produce photoelectric effect corresponds to the binding energy of electrons on the metal surface.

Photoelectric Effect • Light with minimum frequency needed to eject electrons

Photoelectric Voltage & Current • The energy and speed of ejected electrons depends on the frequency (n) of incident light, which must be greater than the threshold (minimum) value for the metal used. Ee = En – Eo (Eo = minimum energy) Ee = h(ni – no) (no = minimum frequency) = hc(1/li - 1/lo) (lo = longest wavelength) • Speed of electron: ve = (2 Ee/me)½ • The photoelectric voltage is directly related to the energy of ejected electrons, which depends on the frequency of light. • The photoelectric current (or the Amps) depends on the intensity of incident light – higher light intensity produces more current.

Einstein’s Explanation of Photoelectric Effect • Light is composed of energy particles called photon • Energy of each photon is dependent only on the frequency of light emitting the photon: Ep = hn; • Total energy of electromagnetic radiation (light) = Nhn, – where N being the number of photon. • When light strikes on the metal, the photon is absorbed by an electrons on the metal surface, such that one electron absorbs only a photon (a quantum of energy) and the electron becomes excited. • If the photon carries energy greater than the binding energy of the metal, that electron will be ejected from the metal surface. The excess energy becomes the kinetic energy of electron. • Light is considered to have both wave and particle properties

E = mc 2 & E = hc/l l = h/mc • Portrait of Albert Einstein:

Continuous Spectrum • White light produces a continuous spectrum

Atomic Spectrum • Spectrum produced by hydrogen gas discharge contains discrete lines:

Hydrogen Spectrum • Balmer’s equation for hydrogen spectrum in the visible region: 1/l = 1. 097 x 107 m-1(1/22 – 1/n 2); 1/l = 1. 097 x 10 -2 nm-1(1/22 – 1/n 2); (n > 2) • If n = 3, 1/l = 1. 097 x 10 -2 nm-1(1/22 – 1/32) = 1. 524 x 10 -3 nm-1 l = 656. 3 nm If n = 4, 1/l = 1. 097 x 10 -2 nm-1(1/22 – 1/42) = 2. 057 x 10 -3 nm-1 l = 486. 2 nm

General equations for hydrogen spectrum: 1/l = 1. 097 x 107 m-1(1/n 12 – 1/n 22); n = 3. 289 x 1015 s-1(1/n 12 – 1/n 22); (n 1 > 0, n 2 > n 1 )

Spectral Series of Hydrogen Spectrum • Recurring patterns of line spectra for hydrogen were observed in different spectral regions, such as in ultraviolet region, visible region, infrared region, etc. • Spectral lines in ultraviolet region are called the Lyman series, which are due to electronic transitions from higher energy levels to level n = 1; • Spectral lines observed in the visible region, called the Balmer series, are due to electronic transitions from upper energy levels to level n = 2; • Spectral lines that appear in infrared region, called the Paschen series, are due to electronic transitions from upper energy levels to level n = 3.

Balmer’s Equation: 1/l = RH(1/22 – 1/n 2) • Portrait of Johann Balmer:

Electronic Transitions in Hydrogen Discharge • Electronic transitions that produce different sets of line spectra

Bohr’s Model for Hydrogen 1. 2. Electron orbits the nucleus in the manner Earth orbits the Sun Only a particular set of orbits is allowed – each orbit must satisfy the condition that the angular momentum: mever = nh/2 p (r = orbit radius) 3. While in a particular orbit, electron neither gains nor loses energy each orbit is called stationary state 4. Electronic energy in a given orbit is given by the expression: En = -2. 18 x 10 -18 J(1/n 2) (n = 1, 2, 3, …. ) 5. Electron gains energy when it jumps from an inner orbit to the outer orbit, and loses energy when it jumps from an outer orbit to an inner one, such that, DE = -2. 18 x 10 -18 J (1/nf 2 - 1/ni 2); (n = 1, 2, 3, …)

Energy in Hydrogen Atom: En = -B(Z 2/n 2) • Portrait of Niels Bohr:

“Electrons occupy discrete orbits of constant energy. These orbits are described using the ordinary mechanics, while the passing of the system between different stationary states cannot be treated on this basis” * Niels Bohr, “On the Constitution of Atoms and Molecules” Philosophical Magazine and Journal of Science, Series 6, Vol. 26, No. 151, pp. 1 -25

“In making a transition between stationary states, a single photon will be radiated…” * Niels Bohr, “On the Constitution of Atoms and Molecules” Philosophical Magazine and Journal of Science, Series 6, Vol. 26, No. 151, pp. 1 -25

Applying Bohr’s Model to Hydrogen Atom • Consider an electron jumps from energy levels n = 3 to n = 2: • Ei = E 3 = -2. 178 x 10 -18 J(1/32) = -2. 420 x 10 -19 J • Ef = E 2 = -2. 178 x 10 -18 J(1/22) = -5. 445 x 10 -19 J DE = E 2 – E 3 = -2. 178 x 10 -18 J(1/22 - 1/32) = -3. 025 x x 10 -19 J • Energy lost by electron is emitted as radiation energy, En = hc/l l = hc/En = (6. 626 x 10 -34 J. s)(2. 998 x 108 m/s)/(3. 025 x 10 -19 J) • = 6. 567 x 10 -7 m = 656. 7 nm • Calculated wavelength agrees with observed values of alpha (red) line in hydrogen spectrum. • When electron jumps from levels n = 4 to n = 2, emitted photon calculated wavelength agrees with the beta (blue) line in H-spectrum with l = 486. 4 nm.

Limitation of Bohr’s Model • Bohr’s model works only for hydrogen atom and other one-electron (hydrogen-like) ionic species, such as He+, Li 2+, etc. • For H-atom, Bohr’s energy given by: En = -2. 178 x 10 -18 J(1/n 2) • For other one-electron particle energy given by: En = -2. 178 x 10 -18 J(Z 2/n 2) • Bohr’s model cannot explain atomic spectra of atoms having more than one electron;

Traveling and Standing Waves • Light waves are traveling waves – values of wavelengths and frequencies are infinite • Waves on plucked strings (guitar, violin, cello, etc. ) are standing waves – their motions limited within a boundary • The wavelengths of a standing wave is limited by the length of the string – that is, l = 2 L/n L = distance the wave has to travel within a boundary and n = 1, 2, 3, …(integer) • Standing waves are quantized – the wavelength has certain fixed values (not arbitrary values) that are limited by 2 L/n.

Traveling Waves

Defined Wavelength for Standing Waves

Standing Wave

Particle-Wave Duality • According to Einstein, light can be both particle and wave. • Louis de Broglie proposed that other particles too can have both particulate and wave properties. • He proposed that a particle with mass m traveling at a speed v will exhibit a wavelength given by the following formula: l = h/mv (h is Planck constant) For example, an electron (me = 9. 11 x 10 -31 kg) traveling at 3. 00 x 107 m/s acquires a wave characteristic such that, l = (6. 626 x 10 -34 J. s)/{(9. 11 x 10 -31 kg)(3. 00 x 108 m/s)} = 2. 42 x 10 -11 m = 24. 2 pm

De Broglie’s Equation: l = h/mv • Portrait of Louis de Broglie:

Heisenberg Uncertainty Principle • • • It is impossible to know simultaneously both the exact location and the energy of an electron in a given atom. If the momentum or energy of an electron is determined accurately, then the knowledge of its location becomes less precise. Heisenberg’s uncertainty principle can be expressed as: Dx. (m. Dv) > h/4 p; where Dx represent uncertainty in determining the location and Dv represents the uncertainty in the speed (Such uncertainty is insignificant in macroscopic objects, but becomes very dominant when applied to a subatomic system. ) According to Heisenberg Uncertainty principle, it is not appropriate to assume that electrons are moving around the nucleus in a well-defined orbit, as stated in the Bohr’s model.

Heisenberg Uncertainty: Dx. Dp > h/4 p • Portrait of Werner Heisenberg:

Quantum Mechanical Model • Also called wave mechanics – treating all motions of particles as wave-like; • Louis de Broglie originated the idea that, like light, all particulate motions have wave characteristics; – a new mathematical formula that incorporates both particulate and wave characteristics was needed. • Heisenberg uncertainty principle implies that we cannot know the position and energy of an electron in atom at the same time with some degree of certainty. – If we determine precisely the energy of electrons in atoms, we can only approximate their where about • Erwin Shrödinger derived a mathematical model for hydrogen that assumed electron to behave a standing wave.

Schrödinger’s Wave Function, (x, y, z) • (h 2/8 p 2 me)[(d 2 /dx 2) + (d 2 /dy 2) + (d 2 /dz 2)] – (Zq 1 q 2/r) = E • The equation is a bit complicated and Schrödinger wasn’t even sure if it works • We’ll try to understand the meaning of this equation • The wave function (x, y, z) has no physical meaning, but • [ (x, y, z)]2 implies probability • The square of the wave function yields a probability about finding an electron having a particular energy at a given location in the atom – just probability, not a definite location. • The sum of the squares of these wave functions yields a probability space called orbital.

Orbitals • Orbital 1. 2. 3. 4. It is a probability space inside the atom where the chances of finding an electron with particular energy value is greater than 90% Each orbital is described by a set of three quantum numbers: n, l, and ml ; The number of orbitals in a subshell is equal to (2 l + 1) and the number of orbitals in a shell is equal to n 2; As a consequence of the Pauli exclusion principle, each orbital can accommodate a maximum of two electrons, which must have opposite spins

Quantum Numbers • A set of numbers that describe an orbital or an electron • The principal quantum number (n) has the integral values: 1, 2, 3, …, ∞. It is related to the size and energy of the orbital • The angular momentum quantum number (l) has the integral values: 0, 1, 2, …, (n – 1). It is related to the shape of atomic orbitals. Each value of l is designated a letter symbol, which is summarized below: – Values of l: 0 1 2 3 – Letter symbols: s p d f • The magnetic quantum number (ml) is related to the orientation of the orbital in the Cartesian coordinates x, y, and z. – ml has values from – l to +l (including 0)

Other Meanings of The Quantum Numbers • • The principal quantum number (n) also describes the primary electronic shell or main energy level The angular momentum quantum number (l) also implies the subshell or energy sub-level The number of sub-shell in a given energy shell is equal to n: 1. Shell n = 1 has one subshell - the 1 s-subshell; 2. shell n = 2 has two subshells - the 2 s- and 2 p-subshells; 3. shell n = 3, has three subshells - the 3 s-, 3 p-, and 3 d-subshells, and so on, … The number of orbitals in a given subshell is determined by the possible values that ml can have, which is equal to (2 l + 1): – subshell l = 0 has one orbital; l = 1 has three orbitals; l = 2 has five orbitals; l = 3 has seven orbitals, and so on…

Quantum Numbers and Orbital Designations • • • The combination of quantum numbers: n, l, and ml, describes a particular orbital in the atom. 1. n = 1, l = 0, and ml = 0, orbital 1 s; 2. n = 2, l = 0, and ml = 0, orbital 2 s; 3. n = 3, l = 0, and ml = 0, orbital 3 s; 4. n = 2, l = 1, and ml = 0, orbital 2 p; 5. n = 3, l = 1, and ml = 0, orbital 3 p; 6. n = 3, l = 2, and ml = 0, orbital 3 d; All orbitals with l = 0 have spherical shape, but the size becomes larger as the value of n increases; Each orbital-p has two lobes, like a dumb-bell, with a nodal plane

Radial Probability Distribution for 1 s in Hydrogen

Radial Probability Distributions for 1 s, 2 s & 2 p in Hydrogen

Radial Probability Distributions of s and p

Radial Probability Distributions of 3 d and 4 s

Atomic Orbitals 1 s, 2 pz, 2 py, and 2 px

Atomic Orbitals: 1 s, 2 p and 3 d

Experiment by Stern & Gerlac Led to The Concept of Electron Spins

The Spinning Electrons

Quantum Numbers To Describe Electrons in Atoms and The Limitation Set By Pauli Exclusion Principle • Sets of three quantum numbers: n, l, and ml, are needed to describe atomic orbitals; • A fourth quantum number - the spin quantum number (ms), is also needed to describe an electron in an atom. • The spin quantum number (ms) is assigned values +½ or -½, which denote spin direction clockwise or counter-clockwise • Pauli Exclusion Principle suggests that two electrons in a given atom cannot have the same set of four quantum numbers – at least one of the quantum numbers must be different. • Consequently, an orbital can accommodate only two electrons with opposite spins.

Energy of Orbitals and Electrons in Hydrogen and Multi-electrons Atoms • In hydrogen atom and other hydrogen-like ions, the energy of orbitals are defined only by the principal quantum number (n). • In multi-electrons atoms and ions, the energy of orbitals are primarily defined by the principal quantum number, n, but it is also influenced (to some extent) by the angular momentum quantum number (l). • Energy trend in multi-electrons atoms: 1 s < 2 p < 3 s < 3 p < 4 s < 3 d < 4 p < 5 s < 4 d < 5 p < 6 s < 4 f < 5 d < 6 p < 7 s < 5 f < 6 d < 7 p;

Developing The Ground State Electron Configurations for Multi-electrons Atoms • The Aufbau method suggests that electrons be assigned to orbitals starting with the lowest energy; • Pauli Exclusion Principle must be obeyed; a maximum of two electrons are assigned to each orbital; • The total number of electrons in a shell or sub-shell depends on the number of orbitals in it; * For a given shell n, there are n 2 number of orbitals, and the maximum number of electrons in that shell is 2 n 2. • Hund’s Rule: If a sub-shell contains degenerate orbitals (orbitals having the same energy), such as 2 p, 3 d, etc. , each orbital must be assigned an electron with the same spin before the second electron is added to it.

Electron Configuration of Multi-Electron Atoms • He (Z = 2): 1 s 2 • • Li (Z = 3): 1 s 2 2 s 1 Be (Z = 4): 1 s 2 2 s 2 B (Z = 5): 1 s 2 2 p 1 C (Z = 6): 1 s 2 2 p 2 N (Z = 7): 1 s 2 2 p 3 O (Z = 8): 1 s 2 2 p 4 F (Z = 9): 1 s 2 2 p 5 Ne (Z = 10): 1 s 2 2 p 6

Electron Configurations for Elements in The Third Period • • Na (Z = 11): 1 s 2 2 p 6 3 s 1 = [Ne] 3 s 1 Mg (Z = 12): [Ne] 3 s 2 Al (Z = 13): [Ne] 3 s 2 3 p 1 Si (Z = 14): [Ne] 3 s 2 3 p 2 P (Z = 15): [Ne] 3 s 2 3 p 3 S (Z = 16): [Ne] 3 s 2 3 p 4 Cl (Z = 17): [Ne] 3 s 2 3 p 5 Ar (Z = 18): [Ne] 3 s 2 3 p 6

Electron Configurations for Transition Metals • • • Sc (Z = 21): [Ar] 4 s 2 3 d 1 ([Ar] = 1 s 2 2 p 6 3 s 2 3 p 6) Ti (Z = 22): [Ar] 4 s 2 3 d 2 V (Z = 23): [Ar] 4 s 2 3 d 3 *Cr (Z = 24): [Ar] 4 s 1 3 d 5 Mn (Z = 25): [Ar] 4 s 2 3 d 5 Fe (Z = 26): [Ar] 4 s 2 3 d 6 Co (Z = 27): [Ar] 4 s 2 3 d 7 Ni (Z = 28): [Ar] 4 s 2 3 d 8 *Cu (Z = 29): [Ar] 4 s 1 3 d 10 Zn (Z = 30): [Ar] 4 s 2 3 d 10

Periodic Table

The spdf Blocks of Periodic Table

Main Group Elements

Electron Configurations of Valence-Shells • Elements in the same group have the same valence-shell electron configurations – thus explains the similarity in their properties. • Groups: Electron Configurations • • 1 A 2 A 3 A 4 A 5 A 6 A 7 A 8 A ns 1 ns 2 np 2 ns 2 np 3 ns 2 np 4 ns 2 np 5 ns 2 np 6

Periodic Trend of Atomic Sizes

Ionization Energy needed to remove an electron from a gaseous atom: • M(g) + Ip M+(g) + e-; • (Ip = ionization potential or ionization energy)

What is Ionization Energy?

The Periodic Trend of Ionization Energy

Ionization Energy of Main Group Elements

Ionization Energies of 3 rd Period Elements

Ionization Energy of Magnesium Mg(g) Mg+(g) + e-; I 1 = 736 k. J/mol Mg+(g) Mg 2+(g) + e-; I 2 = 1445 k. J/mol Mg 2+(g) Mg 3+(g) + e-; I 3 = 7730 k. J/mol Explain the large energy difference between the second (I 2) and third (I 3) ionization energy for magnesium.

Electron Affinity = Energy released when an electron is added to a gaseous atom

Electron Affinity • Electron affinities of the halogen atoms EA (k. J/mol) • F(g) + e- F-(g); -328 k. J/mol • Cl(g) + e- Cl-(g); -349 k. J/mol • Br(g) + e- Br-(g); -325 k. J/mol • I(g) + e- I-(g); -295 k. J/mol

Electron Affinity • Electron affinities of oxygen: O(g) + e- O-(g); DHo = EA 1 = -141 k. J/mol O-(g) + e- O 2 -(g); DHo = EA 2 = 878 k. J/mol O(g) + 2 e- O 2 -(g); DHo = EA = 737 k. J/mol • EA 2 is positive because energy is needed to overcome repulsion force between two negatively charged particles (O- and e-)

Electron Affinity

Electron Affinity Energy released when an electron is added to an atom: X(g) + e- X-(g) + Energy (EA)

Electronegativity The relative ability of bonded atoms to draw (pull) shared electrons closer to its center.

Trend in Electronegativity

Trends of Atomic Properties

Trends in Metallic, Ionic, and Covalent Characters

Periodic Trends in Atomic Properties 1. Which atom is larger, Li or Cs? Why?

Periodic Trends in Atomic Properties • Which atom is larger, Na or Cl? Why?

1. Periodic Trends in Atomic Properties • Rank the following element in order of increasing (smallest to largest) atomic radii: 1. C, N, Mg, Al, and Si; 2. Li, Na, K, Rb, and Cs; 3. Si, P, S, Cl, and Ar;

Periodic Trends in Atomic Properties 1. Which atom requires more energy to remove an electron, Li or Cs? Why?

Periodic Trends in Atomic Properties 1. Which atom requires more energy to remove an electron, Na or Cl? Why?

1. Periodic Trends in Atomic Properties • Rank the following atoms in order of increasing ionization energy. 1. Al, Si, P, S, Cl; 2. Li, Na, K, Rb, Cs; 3. Al, C, Ca, Mg, N;

Periodic Trends in Atomic Properties 1. Atom A has valence electrons that are lower in energy than the valence electrons of Atom B. Which atom has the higher ionization energy? Explain.

Periodic Trends in Atomic Properties • Which of the following processes requires the most energy? Explain your choice. 1. Na(g) Na+(g) + e-; 2. Na+(g) Na 2+(g) + e-; 3. Mg(g) Mg+(g) + e-; 4. Mg+(g) Mg 2+(g) + e-;

Periodic Trends in Atomic Properties • Which of the following reaction releases the most energy? 1. N(g) + e- N-(g) 2. F(g) + e- F-(g) 3. Cl(g) + e- Cl-(g) 4. Br(g) + e- Br-(g)

Periodic Trends in Atomic Properties 1. The first ionization energy for a given atom in Group 2 is “x. ” A good estimate for the second ionization energy of this atom is: (defend your answer) a. Less than “x. ” It is easier to remove the second electron since this gives the species a noble gas electron configuration. b. About “ 2 x. ” The second electron is harder to remove than the first electron. (See next slide)

Periodic Trends in Atomic Properties (contd) c. About “x. ” Since the electrons are taken from the same energy level, the ionization energies are about the same. d. About “-x. ” The ionization energy is exothermic since the Group 2 atoms want to lose two electrons to achieve a noble gas electron configuration. e. About “-2 x. ” The ionization energy is very exothermic since the Group 2 atoms want to lose two electrons to achieve a noble gas electron configuration.

Periodic Trends in Atomic Properties 1. In going across a row of the periodic table, protons and electrons are being added and atomic radius generally decreases; For example, fluorine has a smaller radius than lithium. 2. In going down a column of the periodic table, protons and electrons are also being added, but the atomic radius generally increases; For example, iodine is larger than fluorine. 3. Explain why this is true.

Periodic Trends in Atomic Properties 1. Which is larger, the hydrogen 1 s orbital or the Li 1 s orbital? Why? 2. Which is lower in energy, the hydrogen 1 s orbital or the Li 1 s orbital? Why?