Electron Arrangement - Part 1

Transcription

1 Brad Collins Electron Arrangement - Part 1 Chapter 8 Some images Copyright The McGraw-Hill Companies, Inc.

2 Properties of Waves Wavelength (λ) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. 8.1

3 Properties of Waves (λ) Frequency (ν) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (u) of the wave = λ x ν 8.1

4 Maxwell (1873), proposed that visible light consists of electromagnetic waves. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 108 m/s ALL electromagnetic radiation: c = λ ν 8.1

5 Types of Electromagnetic (EM) Radiation 8.1

6 A photon has a frequency of 6.0 x 10 4 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? λ c = λ ν λ = c ν λ = 3.00 x 10 8 m/s 6.0 x 10 4 s 1 λ 5.0 x 10 3 m 1m = 1 x 10 9 nm λ = 5.0 x 10 3 m 10 9 nm/m λ = nm ν 8.1

7 Particle Behavior of Light Max Planck (1900) found that energy is related to wavelength. Shorter wavelengths have higher frequencies and higher energy Expressed as E = constant frequency (ν) Planck s constant (h) is the smallest unit of energy Energy exists in discrete units with energies that are integer multiples of hν. Energy is gained or lost in integer (n) multiples of h ν E = n h ν Energy (light) is emitted or absorbed in discrete units (quanta). 8.1

8 Photoelectric Effect The photoelectric effect is the ability of light to dislodge electrons from a metal surface. If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal. The electrons will only be ejected once the threshold frequency is reached. Below the threshold frequency, no electrons are ejected. Above the threshold frequency, the number of electrons ejected depends on the intensity of the light. The photoelectric effect provides evidence for the particle nature of light -- quantization. 8.1

9 Particle Nature of Light Photoelectric Effect Solved by Einstein, 1905 h Light has dual nature Wave nature, c = λ ν Particle nature, E = h ν KE A photon is a particle or quanta of light A photon has energy, E = h ν Electrons are held in the metal with binding energy, BE The kinetic energy (KE) of the ejected electron: KE(electron) = hν(photon) BE(electron) To eject an electron, a photon must have more energy than the BE of the electron. 8.1

10 The Bohr Model Emission Spectra of Elements Radiation composed of only one wavelength is called monochromatic. Radiation that spans a whole array of different wavelengths is called continuous. White light can be separated into a continuous spectrum of colors. Elements do not emit light in a continuous spectrum 8.2

11 Continuous Spectrum of Light Note that there are no dark regions in the continuous spectrum that would correspond to different lines. White Light 8.2

12 Line Spectrum of Elements Line Emission Spectrum of Hydrogen Atoms 8.2

13 8.2

14 The Rydberg Equation Johannes Rydberg found hydrogen emission lines could be described using an equation:!! 1 ( 1 = λ 1 ) na 2 na 2 where RH is a constant = x 10 7 m 1 and na and nb are two whole number integers Based on measurements - empirical Why does this equation work? 8.2

15 Bohr Model of the Atom Neils Bohr Believed electron energy is quantized Electrons can only have specific, quantized energy values, E n * E n = B/n 2 B is constant = 2.18 x J n is one of the quantized energy levels, n = 1, 2, 3, etc. Light is emitted when an electron moves from a higher energy value to a lower one. *Sign is negative to indicate that electrons in the atom have lower energy than free electrons (infinitely far from the nucleus) Excited State Ground State 8.2

16 E = hν E = hν 8.2

17 Bohr Model of the Atom E(photon) = E = Ef Ei Ef = B/n 2 f n i = 3 n i = 2 n i = 3 n f = 2 Ei = B/n 2 i E = B/n 2 f ( B/n 2 i) E = B (1/n 2 i 1/n 2 f) n f = 1 8.2

18 Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. Energy of Photon E(photon) = E = B (1/n 2 i 1/n 2 f) E(photon) = J (1/25 1/9) E(photon) = J ( ) E(photon) = J Wavelength of Photon E(photon) = h ν, ν = c/λ, so: E(photon) = h c/λ λ = h c/e(photon) λ = ( J s m/s)/ J λ = m * 10 9 nm/m λ = 1280 nm 8.2

19 The Dual Nature of Electrons Why is electron energy quantized? Louis de Broglie, 1924 Electron is both a particle and a wave Electrons behave as standing waves Circumference (2 π r) of the electron s standing wave is given by: 2 π r = n λ = n h/m u where u = velocity of electron m = mass of electron 8.3

20 Practice Problem What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s? λ = h/mu h in J s m in kg u in (m/s) λ = 6.63 x / (2.5 x 10-3 x 15.6) λ = 1.7 x m = 1.7 x nm 8.3

21 The Schrödinger Wave Equation Heisenberg s Uncertainty Principle: on the mass scale of atomic particles we cannot determine the exact location AND momentum of a particle simultaneously If Δx is the uncertainty in position and Δmv is the uncertainty in momentum, then: x mv = h/4 π If the position, x is known precisely ( x is small), then the momentum (mv) value will be known less precisely ( mv will be large). Uncertainty + wave nature means we cannot describe an electron s orbit the same way we would a satellite or planet. Instead we describe the probability of finding an electron in a region around the nucleus. (Schrödinger Wave Equation) 8.3

22 The Quantum Model Schrödinger s wave equation (Ψ) describes wave and particle nature of electrons Ψ is a function of 4 properties: Ψ = fn(n, l, m l, m s ) where n, l, m l, m s are called quantum numbers The 4 quantum numbers are the address of the electron Schrödinger s wave equation describes the energy of an electron, and the probability of finding an electron in a region of space outside the nucleus. Schrödinger s wave equation can only be solved exactly for the hydrogen atom. For multi-electron atoms the solution must be approximated. 8.4

23 Quantum Numbers n is the Principal Quantum Number Same as Rydberg s n and Bohr s n Defines energy level (shell) of the electron n = 1, 2, 3, etc. n corresponds to the distance from the nucleus Shells are sometimes given letter-names 8.4

24 Quantum Numbers l is the Angular Momentum Quantum Number l describes the number and type of sub-levels (subshells) in a given shell and the shape of the volume of space that the electron occupies. l = 0, 1, n-1!!!!! n Allowed l s Translation 1 0 one subshell in first shell 2 0, 1 two subshells in second shell 3 0, 1, 2 three subshells in third shell 4 0, 1, 2, 3 four subshells in fourth shell Types of subshells l = 0, 1, are given letter names!!! Subshell nomenclature: Call l = 0 orbital type in the first (n=1) energy shell, 1s l etc symbol! s p d f g h 8.4

25 Subshell Shapes When l = 0, shape is spherical l = 0 (s orbitals) 8.4

26 Subshell Shapes When l = 1, shape is dumbbell l = 1 (p orbitals) 8.4

27 Subshell Shapes When l = 2, shape is (mostly) cloverleaf l = 2 (d orbitals) 8.4

28 Quantum Numbers m l is the Magnetic Quantum Number Describes the number of orbitals in a subshell and their orientation in space m l can have values of l 0 +l subshell Allowed m l s Translation s (l = 0) 0 one s-orbital p (l = 1) 1, 0, 1 three p-orbitals d (l = 2) 2, 1, 0, 1, 2 five d-orbitals f (l = 3) 3, 2, 1, 0, 1, 2, 3 7 f-orbitals 8.4

29 m l = -1 m l = 0 m l = 1 m l = -2 m l = -1 m l = 0 m l = 1 m l = 2 8.4

30 Quantum Numbers and Orbitals 8.4

31 Quantum Numbers ms is the Electron Spin Quantum Number Describes the 2 possible spins of an electron Spin gives rise to a magnetic field 2 possible fields: Values of ms = +½, ½ m s = +½ m s = -½ 8.4

32 Schrödinger Consequences Each set of 4 quantum numbers describes the existence and energy of each electron in an atom. Pauli Exclusion Principal: No 2 electrons in an atom can have the same 4 quantum numbers. In a stadium each seat is identified by section, row, and seat numbers. S1, R42, S15 Only 1 person per seat Only 1 electron per set of 4 quantum numbers 8.4

33 Schrödinger Summary Electrons with the same n, occupy the same shell Electrons with the same n and l, occupy the same subshell Electrons with the same n, l, and m l, occupy the same orbital Practice Problem How many electrons can one orbital hold?! If n, l, and m l are fixed, ms can be +½ or ½ So, electrons in a single orbital can have the quantum numbers: n, l, and m l, +½ or n, l, and m l, ½ Answer: 2 electrons 8.4

34 Practice Problem How many 2p orbitals are there in an atom? n=2 2p l = 1 p -type orbitals mean l = 1, so m l = 1, 0 or +1 Answer: 3 orbitals 8.4

35 Practice Problem How many electrons can be placed in the 3d subshell? n=3 3d l = 2 If l = 2, then m l = 2, 1, 0, +1, +2 5 orbitals, each with 2 electrons Total = 10 electrons 8.4

36 Bohr s Model Revisited Hydrogen (1 electron) n = 4 4s 4p 4p 4p 4d 4d 4d 4d 4d n = 3 3s 3p 3p 3p 3d 3d 3d 3d 3d n = 2 2s 2p 2p 2p Orbitals on the same level are degenerate (all types have the same energy) n = 1 1s 8.4

37 Bohr s Model Revisited Multi-electron 4d 4d 4d 4d 4d n = 4 4s 4p 4p 4p 3d 3d 3d 3d 3d n = 3 3p 3p 3p 3s n = 2 2s Transitions from 3s or 3p have different E values. Orbitals on the same level are split (types have different energy) Split energy levels lead to more emission lines. n = 1 1s 2p 2p 2p 8.4