Ch. 7 Atomic and Electronic StructureElectromagnetic Radiation and Atomic Spectra1. Electromagnetic Radiation -- Light

wavelength: (m) frequency: (Hz = s–1)

= c = speed of light = 3.00 x 108 m/s memorize!

memorize!

Wave/Particle Duality• Light was originally viewed as waves, since it displays

diffraction and interference properties. But, it also acts like particles, called photons (h), in some ways.

• Electrons were originally viewed as particles, with a finite mass. But they have interference and can diffract, so they have wavelike properties too.

• de Broglie wavelength:

= h/mv

where = wavelength, h = Planck’s constant (6.626 x 10–34 J•s), m = mass, v = velocity

memorize!

Radiation and the Atom• Energy of electromagnetic radiation

– Radiation interacts with matter in discrete “packets” of energy called “quanta” or “photons”

– E = h where h = Planck’s constant = 6.626 x 10–34 J s– Atomic spectra:

Energetically excited atoms only emit radiation in discrete energies corresponding to the atom’s electronic energy levels.

• Bohr model of H atom– Energy levels E = – b/n2

where b = 2.18 x 10–18 J– Where n is a “quantum number” with possible values of n = 1,2,3,4,…

– Increasing value of n indicates an electron “orbit” farther from the nucleus

It is possible to calculate energy differences between levels (i.e. the atomic spectrum) with different n values by using the Rydberg Equation -- see textbook (but don’t memorize!)

Sample Questions• Calculate the wavelength of an FM radiowave at 100.2 MHz.

• The energy required to ionize sodium is 496 kJ/mol. What is the minimum frequency of light required to ionize sodium?

Sample Questions• Calculate the wavelength of an FM radiowave at 100.2 MHz.

2.99 m

• The energy required to ionize sodium is 496 kJ/mol. What is the minimum frequency of light required to ionize sodium?

1.24 x 1015 Hz

Electron ProbabilityHeisenberg’s Uncertainty Principle states

x • mv = h/4 (do not memorize)

where x is the uncertainty in the position and v is the uncertainty in the velocity, m = mass, h = Planck’s constant

This says that electrons cannot be precisely located and their velocity known at the same time. However, the probability of an electron being in a location can be related to its energy using the Schrodinger equation:

H = Ewhere H = hamiltonian operator, E = energy, and = wavefunction

•Solutions to this equation generate the quantum numbers and define the electron orbitals.

Electronic Quantum Numbers• Electrons in multi-electron atoms can be classified into a

series of:shells ---> subshells ---> orbitals

• Each orbital can be described mathematically by a “wave function” that is characterized by a set of quantum numbers.

• 1. Principal Quantum Number -- n

– Related to energy of shell and to distance from nucleus (size)

– Possible values of n = 1, 2, 3, 4, …

Electronic Quantum Numbers• 2. Secondary Quantum Number -- l

– Related to shape of various subshells within a given shell

– Possible values of l = 0, 1, 2, 3, 4, … n-1

• Letter designation: s, p, d, f, g, …

Values of n Values of l subshells1 0 1s2 0, 1 2s, 2p3 0, 1, 2 3s, 3p, 3d

Electronic Quantum Numbers• 3. Magnetic Quantum Number -- ml

– related to spatial orientation of orbitals within a given subshell

– possible values of ml = –l, … 0, … +l

– the number of ml values = number of orbitals within a subshell

e.g. within a subshell having l = 2, there are 5 orbitals corresponding to the 5 possible values of ml (-2, -1, 0, +1, +2)

Electronic Quantum Numbers Summary -- electronic quantum numbers and orbitals

n l ml subshell # orbitals

1 0 0 1s 1

2 0 0 2s 1 1 -1. 0, +1 2p 3

3 0 0 3s 1 1 -1, 0, +1 3p 3 2 -2, -1, 0, +1, +2 3d 5

4 0 0 4s 1 1 -1, 0, +1 4p 3 2 -2, -1, 0, +1, +2 4d 5 3 -3, -2, -1, 0, +1, +2, +3 4f 7

Sample Questions• For an electron in a 5f atomic orbital, give all possible

values of the quantum numbers.

• What is the maximum number of orbitals in the 5f subshell?

Sample Questions• For an electron in a 5f atomic orbital, give all possible

values of the quantum numbers.Answer:n = 5l = 3ml = -3, -2, -1, 0, +1, +2, +3

• What is the maximum number of orbitals in the 5f subshell?

Answer: 7

Shapes of Atomic OrbitalsAtomic orbitals are best viewed as “clouds of electron density” and

represented as contour plots of the probability of finding the electron.

nodal surface an imaginary point, plane, or spherical surface where the probability of finding

the electron is equal to zerosimplified pictures:

s orbitals are spherical shaped

Shapes of Atomic Orbitalsp orbitals are “bow tie” shaped and oriented along the coordinate

axes

px py pz

x

yz

Shapes of Atomic Orbitals

d orbitals have more complex shapes

Orbital Phases –phases alternate just like in 2-D waves; always draw orbitals with “shaded” and “unshaded” lobes. (will be important in bonding)