# Atomic structure The product of frequency and wavelength for all forms of electromagnetic radiation (light) is a constant, the speed of light c.

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1 Chapter 5: Electrons in Atoms Light (Electromagnetic Radiation) Light has the properties of both waves and particles. Light waves carry energy through space. wavelength (λ) meters frequency (ν) Hz (s -1 ) amplitude (a) intensity All light travels at the same speed, c.9979 x 10 8 m/sec (vacuum) The product of frequency and wavelength for all forms of electromagnetic radiation (light) is a constant, the speed of light c. õ c ë ë õ c and ë c õ frequency and wavelength are inversely related: high frequency corresponds to short wavelength long wavelength corresponds to low frequency The frequency (ν is pronounced nu ) is the number of wavelengths that pass a point in a given period of time. (cycles per second) or s -1 where 1Hz 1s -1 The wavelength (λ is pronounced lambda ) is the distance between wave crests in meters (m, cm, nm, pm, Å (angstrom, m)) - 1 -

2 The Electromagnetic Spectrum Example: What wavelengths correspond to FM radio (MHz) signals? What frequencies correspond to microwaves? ë õ c c ë õ m ë s 6 10 Hz 1s 93.5 MHz 1 MHz Hz 1 3.1m ë õ c c õ ë m õ s m 1ìm 1ìm Hz Mz - -

3 Properties of waves: (a) Constructive inference: When waves that are in phase interact, they do so such that the amplitudes add in a positive manner. (b) Destructive Interference: When waves that are out of phase interact, they do so such that the amplitudes cancel one another. Ultraviolet Catastrophe Classically, the intensity of light should increase with decreasing wavelength. If this were so, the intensity of UV light would go to infinity with decreasing wavelength. I order to explain the observations of black-body radiation, Planck surmised that light is released in defined packets or quanta. Light and Energy: Planck s Law Planck s Law: Energy is discontinuous; the transmission of energy can only occur in finite amounts or Quanta E photon h ν h Planck s constant 6.66 x J s Planck s Law is based on the phenomenon known as the - 3 -

4 As the frequency of light increases, the energy increases. As the wavelength of light increases, the energy decreases. Bond energies also correspond to the energies of individual photons. The process of light breaking chemical bonds is known as photodissociation. E photon hc h ν λ Red Light (650 nm) E -34 hc Js ë 1m 650 nm 9 10 nm 8 m s 3.06 photon J photon Blue Light (400 nm) hc Js m E s photon ë 1m 400 nm 9 10 nm Calculate the energy of a mole of photons of 400 nm light. E photon hc ë J s m 400 nm 9 10 nm mole J photons m s -19 J photon photons mole photons kj 1 mol H mol 6.0x10 H E photon hc ë H 10 J 7.4 x 10 photon kj hc ë E J s ë -19 J 7.4 x 10 photon photon m -19 or 75 nm J photon 8 ms

5 Quantum Theory: Atomic Spectra: Atomic Spectrum When a discharge is passed through a tube filled with He, the light emitted spreads into a series of lines rather than a normal spectrum of light. This indicates that something in the atom is not governed by a continuum Something is Quantized! Recall that Quantization was used to explain the Ultraviolet Catastrophe (Planck) Einstein s work on the Photoelectric Effect also contributed to the concept of quantization. When light strikes the surface of certain metals, electrons may be ejected. The light must be of a certain frequency (color) in order for this to occur. The behavior exhibits a threshold effect such that below a minimum energy, no electrons are ejected

6 The threshold behavior for the Photo-electric Effect Since E hν Only photons of frequency greater than the minimum frequency (ν o ) can eject electrons Any excess energy from the photon goes into the kinetic energy of the electron. ν (photon) ν o electrons are removed with no KE ν (photon) > ν o electrons are ejected Example: A certain metal has a threshold frequency (ν o ) of 3.66 x s -1. Will 53 nm light cause electrons to be ejected? E (electron) E (photon) - Φ if ν (photon) > ν o then electrons are ejected ν λ c E (electron) E (photon) - Φ ½ m e v E (photon) hν m e 9.11 x kg v velocity of the ejected electrons Φ ejecton threshold Work function í c ë 8 m s m 53 nm x 9 10 nm ν (photon) > ν o s What is the velocity of the ejected electrons? -1 Electron are ejected ν o Φ/h If ν (photon) < ν o Threshold frequency no electrons are ejected E (electron) E (photon) - Φ ½ m e v - 6 -

7 1 m hc ë hí o 1 m v e v 6.66 x 10 J s x 3.00 x 10 1m 53 nm x 9 10 nm 6.66 x 10 e v hc - hí ë o x x 10 x 9.11x 10 J s x 3.66x J J kg 8 14 m s s x x 10 m s J J The Bohr Atom: The concept of the atom derived form the Rutherford gold film experiment failed to explain hoe the electrons ordered them selves about the nucleus. In 1913, Niels Bohr proposed a model for electron distributions that was a combination of classical and the new emerging quantum theories. 1. Electrons move in circular orbits about the nucleus.. These orbits are fixed or discrete in terms of allowed energies governed by states of angular momentum. 3. Electrons can only pass between these allowed levels and nowhere in between. Conclusion: The energy levels of the electrons are quantized! This explains the observance of line spectra in atom emission. To explain the spectral line puzzle, Bohr came up with a radical model of the atom, which Z had electrons orbiting around a nucleus. i Because of these p "signature colors or emission lines, Bohr stated that electrons had p to exist in discrete orbits or quantized levels and that the spectral y lines occurred when the electron jumped between the allowed, levels. Each level is designated e by a Quantum Number, n h n 1,,3,4. infinity the radius of each orbit is given by: r n n a o The Bohr radius a o 0.53 Å or 53 pm - 7 -

8 The energy of each level is given by: - Z R H En Where R H.179 x J n The Bohr Model: r n n a o n 1,, 3, 4 The Energy Levels: H E n - Z R n The Lowest energy level corresponds to n 1 Where, n n 3 n n-1 n 1 Ground State 1 st excited state nd excited state n th excited state - 8 -

9 Absorption and Emission When an electron jumps form a lower state to a higher state, Energy (light) is absorbed. When an electron jumps form a higher state to a lower state, Energy is (light) emitted E n ÄE E fin - Z - E n in R H - R n for H fin - - R n H in Z 1 E photon Emission of Light: Electrons move from a higher level (state) to a lower level (state) ÄE R H 1 n in 1 n fin 1 R H 1 h c λ n in h c h ν λ 1 n fin Absorption of Light: Electrons move from a lower level (state) to a higher level (state) A negative signs indicates emission, positive absorption. The Wave-like Nature of a Particle - 9 -

10 The Wave Particle Duality: Heisenberg Uncertainty Principle: Louis de Broglie in response to Planck & Einstein s assertion that light was particle-like (photon) stated that small particles moving fast could exhibit a characteristic wavelength. E mc hυ mc The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa. p x > h / 4π p uncertainty in momentum (velocity) x uncertainty in position h p λ or hυ c mc p since h h λ p m u (momentum) υ c 1 ë u velocity Classically, i.e., in our macroscopic world, I can measure these two quantities to infinite precision (more or less). There is really no question where something is and what its momentum is. In the Quantum Mechanical world, the idea that we can measure things exactly breaks down, i.e. there is a limit to the precision. This uncertainty leads to many strange things. What is the wavelength associated with an 80g tennis ball (d 8 cm) moving at 115 miles per hour? Compare that to an electron moving at 1/100 the speed of light. For example, in a Quantum Mechanical world, I cannot predict where a particle will be with 100 % certainty. I can only speak in terms of probabilities. h λ λ (tennis ball) x λ m 100 p d λ (electron) x λ m 100 d electron looks like a wave! x % %The A consequence of the Quantum Mechanical nature of the world is that particles can appear in places where they have no right to be (from an ordinary, common sense [classical] point of view)!

11 The results state that there is a probability of finding the particle in space at position x with an uncertainty of x. The location of a particle is given by a localized increase in the amplitude of the wave at position x. Probability Distributions: The mental picture of an electron corresponds to a wave superimposed upon the radial trajectory of a particle orbiting the nucleus. The position of an electron is best described by the image of a dart board: As the Schrödinger Wave Equation is solved time and time again, the position of an electron is found such that each hit builds up a pattern. The build up of hits yields the probability in 3-dimensons for the likelihood of finding and electron about the nucleus. It is these probability functions that give rise to the familiar hydrogen-like orbitals that electrons occupy. Quantum numbers and Electron Orbitals Quantum Numbers are terms that were developed to aid in describing electron behavior according to the Schrödinger equation. Principal Quantum Number n n 1,, 3, 4 up to infinity Azimuthal or Angular Quantum Number l l 0, 1,, 3 up to a maximum of n 1 Magnetic Quantum Number m l m l may take on the value an integer from -l to +l Spin Quantum Number m s m s ± 1/ The Quantum numbers give information about the location of an electron, like an address. The principal quantum number indicates the state where the electron is located, the angular momentum quantum number indicates the town, the magnetic QN is the street address and the spin quantum number corresponds to the right or left side of a duplex

12 for l 0 m l 0 (no orientation) for l 1 m l p x p y p z Each n-level defines a principle energy level or shell. n 1,, 3 and for l m l E n Z R n H Z atomic number of the nucleus and R H Rydberg constant. Each l within an n-level represents a subshell. l 0 s subshell l 1 p subshell l d subshell l 3 f subshell Each l subshell is divided into m l orbitals, where m l designates the spatial orientation of each orbital. (Cartesian coordinates, x, y & z) Each orbital can hold electrons, one designated by m s + ½ and one by m s ½ - 1 -

13 - 13 -

14 Electron Configurations: Multi-electron atoms The ideas presented thus far have focused on the H-atom, a oneelectron system. What happens when there are two or more electrons in an atom? The diagram to the right explains: The innermost electrons screen or shield the nucleus from the view of the outer electrons. The outermost electrons in effect see a charge that is less that the actual charge on the nucleus, Z. Shielding of Electrons: This increase in the ability to penetrate magnifies the ability to screen. The effect of Shielding: In a hydrogen atom, the orbitals are arranged as a function of n only. For each value of n, the l-sub shells are degenerate (of the same energy). Shielding brought upon by the presence of more than one electron causes the orbital energies to split. s-orbitals > p or d-orbitals Increasing Screening The further out an electron exists from the nucleus, the greater the effect of shielding. (There are more electrons to screen the nucleus charge) Since the s-orbitals have no nodal properties at the nucleus, they can penetrate more effectively

15 Electron Configuration of Many Electron Elements The electrons of a many-electron atom occupy the orbitals in accordance with a series of rules. The Pauli Exclusion Principle: Only two electrons with opposite spin can occupy an atomic orbital. Stated another way, no two electrons have the same 4 quantum numbers n, l, m l, m s. In applying this rule, you should realize that an atomic orbital is an energy state. Hund's rule: The result of shielding causes the orbitals to arrange in terms of increasing n + l This results in the 4s-orbital having a lower energy that that of the 3d-orbital Electrons prefer parallel spins in separate orbitals of sub shells. Electrons will fill across a set of degenerate orbitals until forced to pair with opposite spins. The Aufbau (Building up) Principle: n l vs. 3 + Electrons fill from the lowest energy states (orbitals) up. E n + l The Aufbau procedure (filling order of atomic orbitals) is used to work out the electron configurations of all atoms

16 Electron Configurations of the 1 st and nd Period: H 1s 1 C 1s s p He 1s N 1s s p 3 Li 1s s 1 O 1s s p 4 Be 1s s F 1s s p 5 B Z 5 5 electrons B 1s s p 1 Ne 1s s p 6 1s s p 1s s p 1 O Z 8 8 electrons 1s s p

17 Valence Electon Blocks: Electron Configurations continued: Electrons in the outermost shell are called valence electrons. It is the valence electrons determine an atom s chemical properties. Electrons in the inner shells are inner electrons or core electrons. Regions in periodic table are designated as the s-block, p-block, d-block and the f-block

18 Core Notation: [Nobel Gas] nd(n+1)s Some anomolies in filling are seen in the d- elements For d 4 and d 9 elements, an s- electron can jump over to create a ½ filled (d 5 )or completely filled (d 10 ) d- orbital. This lowers the overall energy of the atom. What is the electron configuration of the element as shown on the right? Which electrons are the valence electrons and which are the core electrons? Answers: 1s s p 6 3s 3p 6 P (phosphorous)

19 The formation of the phosphide ion: P (1s s p 6 3s 3 3p 3 ) P 3- (1s s p 6 3s 3 3p 6 ) [Ar] Core electrons Electron Configurations of ions: Valence electrons When an atom gains or loses electrons it becomes an ion. Loss of electrons: Cation Gain of electrons: Anion (+) All group 5 (15) anions (-3) will have the electron configuration of the next Nobles gas. Electron configurations of Transition Metal Ions: The charge states on most transition metals cannot be equated to the electron configurations of the Noble gases. You will see why in chem. C (ch. 4 and 5) The electron configurations of transitions metal cations must be determined from the charge state. (-) Fe 3+ 3 electrons lost Ni + electrons lost and so on. Atoms of group 1, and the non-metals will lose or gain electrons to attain the electron configuration of a Nobel gas (ns np 6 ). Example: ion: Na Sodium forming sodium Na + [Ne] When transition metals ionize, they lose the s-electrons first. This may seem odd as it is opposite to the filling order. From a stability argument, the removal of the s-electrons first results in lower energy configuration when we take into account ionization energies of s vs. p and d electrons. 1s s sp 6 3s 1 1s s sp 6 Examples: 3d 1 4s All group 1 cations (+1) will have the electron configuration of the previous Noble gas. Sc 3+ :

20 Cr 3+ : [Ar] 3d 3 Electron Configurations: Excited States Which of the electron configurations to the right corresponds to phosphorous? Answer: c The rest are excited states of phosphorous

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