1 CHAPTER 10 ELECTRONS IN ATOMS

2 Waves and Energy I. Discrepancies with the Rutherford Model l All the positive charge is in the nucleus.

3 Waves and Energy What keeps the nucleus together? l The electrons circle the nucleus.

4 Waves and Energy –Why don’t they spiral into the nucleus? » Rutherford’s Model is unstable. » Niels Bohr –“Small particles don’t behave like big particles.”

5 Waves and Energy » So how do small particles behave? » Led to the development of a new set of rules (mechanics) to describe these observations. Quantum Mechanics by Erwin Schrodinger

6 Waves and Energy l Light » What is light? –A form of energy. –A source of color –Fast: 186,000 mi/s (3.0 X 10 8 m/s) –Travels through a vacuum.

7 Waves and Energy o There are two ways for energy to travel from place to place. o Particle (Remember a particle is matter o Wave o Which is light? wave

8 (A) Refers to node (peak) of wave. The top peak is the crest, and the bottom peak is the trough

9 B. Refers to lambda  or wavelength of wave. The wavelength is a repeating value. (C) Refers to amplitude (A) (height) of peaks.

10 As the wave moves past a stationary object (bird), it is not moved by the wave itself Wave Motion (Ocean Analogy)

11 Waves and Energy Wavelength ( ) (lambda):Distance between two similar points on consecutive pulses. Frequency  The number of wavelengths that pass a specific point per unit of time. (cycles per second - cps) 1 cps = 1 hertz (hz)

12 Waves and Energy Amplitude (A): The distance from rest to crest. (Maximum disturbance) Relates to the amount of energy carried.

13 Waves and Energy » Visible Light: A portion of the electromagnetic energy spectrum (em wave), order of magnitude

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15 l Long Wavelength = Low Frequency = LOW ENERGY l Short Wavelength = High Frequency = HIGH ENERGY

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17 Waves and Energy » How much energy does light carry? –Max Planck (1900): Determined that energy was directly related to frequency E = h h = 6.63 X j/s » Units of light: PHOTON

18 E = h l E = Energy, in units of Joules (kg·m 2 /s 2 ) l h = Planck’s constant (6.626 x J·s) = frequency, in units of hertz (hz, sec-1) The energy (E ) of electromagnetic radiation is directly proportional to the frequency   of the radiation.

19 Waves and Energy –Described by Einstein as “wave packets”. –Carries a discrete amount of energy (quantum)

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21 Waves and Energy » Spectrograph: –Analysis of light using a spectroscope which breaks light into component frequencies. –Continuous Spectrum l Each color = specific freq & energy. Light is quantized.

22 Spectroscopic analysis of the visible spectrum… produces all of the colors in a continuous spectrum

23 Waves and Energy –Bright Line Spectrum l Each line = a color = a frequency = an energy value. l The spectrum is characteristic of the element.

24 Spectroscopic analysis of the hydrogen spectrum… …produces a “bright line” spectrum

25 The Hydrogen Atom l Hydrogen: The simplest atom. It contains only one electron and produces the simplest line spectrum.

26 The Hydrogen Atom l Observations from spectrum: » The H atom emits light when placed in a gas discharge tube. » The light produces a well- ordered spectrum with systematic spacing.

27 The Hydrogen Atom » Each line represents a specific frequency and energy value. » No value of E exceeds the ionization energy of Hydrogen –E ioniz = energy needed to remove 1 electron

28 The Hydrogen Atom –E ioniz = H -> H + + e -

29 The Hydrogen Atom –E ioniz = H -> H + + e - –E ioniz = 1312 kj

30 The Hydrogen Atom –E ioniz = H -> H + + e - –E ioniz = 1312 kj l Interpretations » Hydrogen before becoming excited has a certain energy condition. » After ionization, the hydrogen ion has a certain energy condition.

31 The Hydrogen Atom » If the H+ recaptures the electron the PE (potential energy) is returned to us in the form of light of frequency (nu). –∆E = Ef - Ei = h » The ∆E observed is always less than 1312 kj.

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33 The Bohr Atom l The hidden staircase. l The Bohr Model » The spectrum is produced without losing the electron. » Accepts Rutherford nucleus » e - arrangement is dependent upon the energy condition of the atom. (Energy of the e - is quantized)

34 This produces bands of light with definite wavelengths. Electron transitions involve jumps of definite amounts of energy.

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36 The Bohr Atom » Only certain “energy levels” are possible. (Stationary States) –Ground state: (n=1), the e- can reside here indefinitely. –Excited states: (n=2,3,4,.. ) » Changes in levels: Requires energy (up) or releases energy as light (down).

37 The Bohr Atom –Orbital: l The region of space around a nucleus in which an electron most likely will be found. l An orbital is a region within an atom where there is a probability of finding an electron.

38 Orbital shapes are defined as the surface that contains 90% of the total electron probability. This is a probability diagram for the s orbital in the first energy level…

39 l Quantum Numbers l Each electron in an atom has a unique set of 4 quantum numbers which describe it. l n=Principal quantum number l M=Angular momentum quantum number L =Magnetic quantum number L =Magnetic quantum number

40 l Principal Quantum Number l Generally symbolized by n, it denotes the shell (energy level) in which the electron is located. l Number of electrons that can fit in a shell: l 2n 2

41 Quantum Numbers: four numbers used to describe the electrons in an atom. The Bohr model one-dimensional model one-dimensional model used one quantum number to describe the electrons used one quantum number to describe the electrons

42 Only the size of the orbit was important, which was described by the n quantum number. Only the size of the orbit was important, which was described by the n quantum number.

43 Erwin Schrodinger described an atomic model with electrons in three dimensions. This model required three coordinates, or three quantum numbers, to describe where electrons could be found.

44 1. Principal (shell) quantum number - n Describes the energy level within the atom. Describes the energy level within the atom. *Energy levels are 1 to 7 Maximum number of electrons in n is 2 n 2Maximum number of electrons in n is 2 n 2

45 2. Momentum (subshell) quantum number - l Describes the sublevel in n *Sublevels in the atoms of the known elements are s - p - d - f *Each energy level has n sublevels. *Sublevels of different energy levels may have overlapping energies.

46 The Bohr Atom Wave Functions: Solutions to the wave equation. If n = 1, 1 2 solutions; 1 Orbital If n = 2, 2 2 solutions; 4 Orbitals If n = 3, 3 2 solutions; 9 Orbitals If n = 4, 4 2 solutions; 16 Orbitals

47 The Bohr Atom n=1, 1 orbital; (1)1s n=2, 4 orbitals; (1)2s, (3)2p » (2p x,2p y,2p z ) n=3, 9 orbitals;(1)3s, (3)3p,(5) 3d n=4, 16 orbitals; (1)4s, (3)4p, (5) 4d, (7)4f.

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49 Orbital filling table

50 l Principal Quantum Number l Generally symbolized by n, it denotes the shell (energy level) in which the electron is located. l Number of electrons that can fit in a shell: l 2n 2

51 Sizes of s orbitals Orbitals of the same shape (s, for instance) grow larger as n increases… Nodes are regions of low probability within an orbital.

52 The Bohr Atom Wave Functions: Solutions to the wave equation. If n = 1, 1 2 solutions; 1 Orbital If n = 2, 2 2 solutions; 4 Orbitals If n = 3, 3 2 solutions; 9 Orbitals If n = 4, 4 2 solutions; 16 Orbitals

53 Angular Momentum Quantum Number The angular momentum quantum number, generally symbolized by l, denotes the orbital (subshell) in which the electron is located.

54 The s orbital has a spherical shape centered around the origin of the three axes in space.

55 Magnetic Quantum Number The magnetic quantum number, generally symbolized by m, denotes the orientation of the electron’s orbital with respect to the three axes in space.

56 Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3. To remember the shapes, think of “double dumbbells” …and a “dumbbell with a donut”!