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Chapter 7: Periodicity and Atomic Structure

Renee Y. Becker

Valencia Community College

CHM 1045

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Light and Electromagnetic Spectrum

• Several types of electromagnetic radiation make up the electromagnetic spectrum

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Light and Electromagnetic Spectrum

Frequency, : The number of wave peaks that pass a given point per unit time (1/s)

Wavelength, : The distance from one wave peak to the next (nm or m)

Amplitude: Height of wave

Wavelength x Frequency = Speed

(m) x (s-1) = c (m/s)

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Light and Electromagnetic Spectrum

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The Planck Equation

E = h E = hc / h = Planck’s constant, 6.626 x 10-34 J s

1 J = 1 kg m2/s2

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Example1: Light and Electromagnetic Spectrum

• The red light in a laser pointer comes from a diode laser that has a wavelength of about 630 nm. What is the frequency of the light? c = 3 x 108 m/s

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Atomic Spectra

• Atomic spectra: Result from excited atoms

emitting light.

• Line spectra: Result from electron transitions

between specific energy levels.

• Blackbody radiation is the visible glow that

solid objects emit when heated.

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Atomic Spectra

• Max Planck (1858–1947): proposed the energy is

only emitted in discrete packets called quanta.

The amount of energy depends on the frequency:

E = energy = frequency

= wavelength c = speed of light

h = planck’s constant

E h

hc h 6.626 10 34J s

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Atomic Spectra

Albert Einstein (1879–1955):

Used the idea of quanta to explain the photoelectric effect.

• He proposed that light behaves as a stream of particles called photons

• A photon’s energy must exceed a minimum threshold for electrons to be ejected.

• Energy of a photon depends only on the frequency.

E = h

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Atomic Spectra

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Example 2: Atomic Spectra

• For red light with a wavelength of about 630 nm, what is the energy of a single photon and one mole of photons?

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Wave–Particle Duality

• Louis de Broglie (1892–1987): Suggested

waves can behave as particles and particles

can behave as waves. This is called wave–

particle duality.

m = mass in kg p = momentum (mc) or (mv)

For Light : h

mch

p

For a Particle : h

mvh

p

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Example 3: Wave–Particle Duality

• How fast must an electron be moving if it has a de Broglie wavelength of 550 nm?

me = 9.109 x 10–31 kg

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Quantum Mechanics

• Niels Bohr (1885–1962): Described atom as

electrons circling around a nucleus and

concluded that electrons have specific energy

levels.

• Erwin Schrödinger (1887–1961): Proposed

quantum mechanical model of atom, which

focuses on wavelike properties of electrons.

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Quantum Mechanics

• Werner Heisenberg (1901–1976): Showed

that it is impossible to know (or measure)

precisely both the position and velocity (or the

momentum) at the same time.

• The simple act of “seeing” an electron would

change its energy and therefore its position.

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Quantum Mechanics

• Erwin Schrödinger (1887–1961): Developed

a compromise which calculates both the

energy of an electron and the probability of

finding an electron at any point in the

molecule.

• This is accomplished by solving the

Schrödinger equation, resulting in the wave

function

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Quantum Numbers

• Wave functions describe the behavior of electrons.

• Each wave function contains four variables called

quantum numbers:

• Principal Quantum Number (n)

• Angular-Momentum Quantum Number (l)

• Magnetic Quantum Number (ml)

• Spin Quantum Number (ms)

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Quantum Numbers

• Principal Quantum Number (n): Defines the

size and energy level of the orbital. n = 1, 2, 3,

– As n increases, the electrons get farther from

the nucleus.

– As n increases, the electrons’ energy

increases.

– Each value of n is generally called a shell.

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Quantum Numbers

• Angular-Momentum Quantum Number (l): Defines the three-dimensional shape of the orbital.

• For an orbital of principal quantum number n, the value of l can have an integer value from

0 to n – 1.

• This gives the subshell notation:

l = 0 = s orbital l = 3 = f orbital

l = 1 = p orbital l = 4 = g orbital

l = 2 = d orbital

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Quantum Numbers

• Magnetic Quantum Number (ml): Defines the spatial orientation of the orbital.

• For orbital of angular-momentum quantum number, l, the value of ml has integer values from –l to +l.

• This gives a spatial orientation of:

l = 0 giving ml = 0

l = 1 giving ml = –1, 0, +1

l = 2 giving ml = –2, –1, 0, 1, 2, and so on…...

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Quantum Numbers

• Magnetic Quantum Number (ml): –l to +l

S orbital 0

P orbital -1 0 1

D orbital -2 -1 0 1 2

F orbital -3 -2 -1 0 1 2 3

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Quantum Numbers

• Spin Quantum

Number: ms

• The Pauli Exclusion

Principle states that no

two electrons can have

the same four quantum

numbers.

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Quantum Numbers

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Example 4: Quantum Numbers

• Why can’t an electron have the following quantum numbers?

(a) n = 2, l = 2, ml = 1

(b) n = 3, l = 0, ml = 3

(c) n = 5, l = –2, ml = 1

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Example 5: Quantum Numbers

• Give orbital notations for electrons with the following quantum numbers:

(a)n = 2, l = 1

(b) n = 4, l = 3

(c) n = 3, l = 2

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Electron Radial Distribution

• s Orbital Shapes: Holds 2 electrons

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Electron Radial Distribution

• p Orbital Shapes: Holds 6 electrons, degenerate

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Electron Radial Distribution

• d and f Orbital Shapes: d holds 10 electrons and f holds 14 electrons, degenerate

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Effective Nuclear Charge

• Electron shielding leads to energy differences among orbitals within a shell.

• Net nuclear charge felt by an electron is called the effective nuclear charge (Zeff).

• Zeff is lower than actual nuclear charge.

• Zeff increases toward nucleus

ns > np > nd > nf

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Effective Nuclear Charge