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CHAPTER 10CHAPTER 10

ELECTRONS IN ELECTRONS IN ATOMSATOMS

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Waves and Energy

I. Discrepancies with I. Discrepancies with the Rutherford Modelthe Rutherford Model

All the positive charge All the positive charge is in the nucleus. is in the nucleus.

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Waves and Energy

What keeps the nucleus What keeps the nucleus together?together?

The electrons circle the The electrons circle the nucleus.nucleus.

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Waves and Energy

–Why donWhy don’’t they spiral into t they spiral into the nucleus?the nucleus?

» RutherfordRutherford’’s Model is s Model is unstable.unstable.

» Niels BohrNiels Bohr–““Small particles donSmall particles don’’t t behave like big particles.behave like big particles.””

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Waves and Energy

»So how do small So how do small particles behave?particles behave?

»Led to the development Led to the development of a new set of rules of a new set of rules (mechanics) to describe (mechanics) to describe these observationsthese observations. . Quantum Mechanics by Erwin Quantum Mechanics by Erwin SchrodingerSchrodinger

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Waves and Energy

Light»What is light?

–A form of energy.–A source of color–Fast: 186,000 mi/s (3.0 X 108 m/s)

–Travels through a vacuum.

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Waves and Energy

o There are two ways for energy to travel from place to place.oParticle (Remember a particle is matter

oWaveo Which is light?

wavewave

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

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B. Refers to lambda B. Refers to lambda or or wavelength of wave. The wavelength of wave. The wavelength is a repeating wavelength is a repeating value.value.

(C) Refers to amplitude (A) (C) Refers to amplitude (A) (height) of peaks.(height) of peaks.

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As the As the wave wave moves past moves past a a stationary stationary object object (bird), it is (bird), it is not moved not moved by the by the wave itselfwave itself

Wave Motion (Ocean Analogy)

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Waves and Energy

Wavelength (Wavelength () ) (lambda):Distance between (lambda):Distance between two similar points on two similar points on consecutive pulses.consecutive pulses.

Frequency Frequency The number of The number of wavelengths that pass a wavelengths that pass a specific point per unit of specific point per unit of time. (cycles per second - time. (cycles per second - cps) cps) 1 cps = 1 hertz1 cps = 1 hertz (hz) (hz)

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Waves and Energy

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

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Waves and Energy

» Visible Light: A portion of the electromagnetic energy spectrum (em wave), order of magnitude 1014.

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Long Wavelength = Low Frequency = LOW ENERGY

Short Wavelength = High Frequency = HIGH ENERGY

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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 10-34 j/s

» Units of light: PHOTON

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E = h E = Energy, in units of Joules

(kg·m2/s2) h = Planck’s constant (6.626 x 10-34

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.

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Waves and Energy

–Described by Einstein as “wave packets”.

–Carries a discrete amount of energy (quantum)

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Waves and Energy

» Spectrograph: –Analysis of light using a spectroscope which breaks light into component frequencies.

–Continuous SpectrumEach color = specific freq & energy. Light is quantized.

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

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Waves and Energy

–Bright Line SpectrumEach line = a color = a frequency = an energy value.

The spectrum is characteristic of the element.

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Spectroscopic analysis of the hydrogen spectrum… …produces a

“bright line” spectrum

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The Hydrogen Atom

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

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The Hydrogen Atom

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.

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The Hydrogen Atom

» Each line represents a specific frequency and energy value.

» No value of E exceeds the ionization energy of Hydrogen

–Eioniz = energy needed to remove 1 electron

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The Hydrogen Atom

–Eioniz = H -> H+ + e-

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The Hydrogen Atom

–Eioniz = H -> H+ + e-

–Eioniz = 1312 kj

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The Hydrogen Atom

–Eioniz = H -> H+ + e-

–Eioniz = 1312 kj Interpretations

» Hydrogen before becoming excited has a certain energy condition.

» After ionization, the hydrogen ion has a certain energy condition.

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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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The Bohr Atom

The hidden staircase. 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)

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This produces bands of light with definite wavelengths.Electron transitionsinvolve jumps of definite amounts of

energy.

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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).

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The Bohr Atom

–Orbital: The region of space around a

nucleus in which an electron most likely will be found.

An orbital is a region within an atom where there is a probability of finding an electron.

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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…

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Quantum NumbersQuantum Numbers Each electron in an atom has a Each electron in an atom has a

unique set of 4 quantum numbers unique set of 4 quantum numbers which describe it.which describe it.

  n=Principal quantum number n=Principal quantum number   M=Angular momentum quantum M=Angular momentum quantum

number number   LL=Magnetic quantum number =Magnetic quantum number

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Principal Quantum Number

Generally symbolized by n, it denotes the shell (energy level) in which the electron is located.

Number of electrons that can fit in a shell:

2n2

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

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• • Only the size of the orbit was Only the size of the orbit was important, which was important, which was described by the described by the nn quantum quantum number. number.

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

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1. Principal (shell) quantum number1. Principal (shell) quantum number - - nn Describes the energy level within Describes the energy level within the atom. the atom. ** Energy levels are 1 to 7 Energy levels are 1 to 7 •Maximum number of electrons in n Maximum number of electrons in n is 2is 2 nn 22

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2. Momentum (subshell) quantum 2. Momentum (subshell) quantum number -number - ll Describes the sublevel inDescribes the sublevel in nn ** Sublevels in the atoms of the Sublevels in the atoms of the known elements known elements are are ss - - pp - - dd - - ff ** Each energy level hasEach energy level has nn sublevels. sublevels. ** Sublevels of different energy levels Sublevels of different energy levels may have overlapping energies. may have overlapping energies.

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The Bohr Atom

Wave Functions: Solutions to the Wave Functions: Solutions to the wave equation.wave equation.If n = 1, 1If n = 1, 122 solutions; 1 Orbital solutions; 1 OrbitalIf n = 2, 2If n = 2, 222 solutions; 4 Orbitals solutions; 4 OrbitalsIf n = 3, 3If n = 3, 322 solutions; 9 Orbitals solutions; 9 OrbitalsIf n = 4, 4If n = 4, 422 solutions; 16 solutions; 16 OrbitalsOrbitals

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The Bohr Atom

n=1, 1 orbital; (1)1sn=1, 1 orbital; (1)1sn=2, 4 orbitals; (1)2s, (3)2pn=2, 4 orbitals; (1)2s, (3)2p

» (2p(2pxx,2p,2pyy,2p,2pzz))n=3, 9 orbitals;(1)3s, (3)3p,(5) n=3, 9 orbitals;(1)3s, (3)3p,(5)

3d3d

n=4, 16 orbitals; (1)4s, (3)4p,n=4, 16 orbitals; (1)4s, (3)4p,(5) (5) 4d, (7)4f.4d, (7)4f.

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Orbital filling table

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Principal Quantum Number

Generally symbolized by n, it denotes the shell (energy level) in which the electron is located.

Number of electrons that can fit in a shell:

2n2

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Sizes of s orbitalsOrbitals of the same shape (s, for instance) grow larger as n increases…

Nodes are regions of low probability within an orbital.

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The Bohr Atom

Wave Functions: Solutions to the Wave Functions: Solutions to the wave equation.wave equation.If n = 1, 1If n = 1, 122 solutions; 1 Orbital solutions; 1 OrbitalIf n = 2, 2If n = 2, 222 solutions; 4 Orbitals solutions; 4 OrbitalsIf n = 3, 3If n = 3, 322 solutions; 9 Orbitals solutions; 9 OrbitalsIf n = 4, 4If n = 4, 422 solutions; 16 solutions; 16 OrbitalsOrbitals

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Angular Momentum Quantum Number

The angular momentum quantum number,

generally symbolized by l, denotes the orbital (subshell) in which the electron is

located.

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The s orbital has a spherical shape centered around

the origin of the three axes in space.

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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.

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