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Chapter 6 Electronic Structure of AtomsPowerPoint Presentation

Chapter 6 Electronic Structure of Atoms

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- All waves have a characteristic wavelength, l, and amplitude, A.
- The frequency, f, of a wave is the number of cycles which pass a point in one second.
- The speed of a wave, v, is given by its frequency multiplied by its wavelength:
- c = fλ
- c is the speed of light

Chapter 6

- Modern atomic theory involves interaction of radiation with matter.
- Electromagnetic radiation moves through a vacuum with a speed of 3.00 108 m/s.

Chapter 6

Electromagnetic spectrum matter.

Example 1: A laser produces radiation with a wavelength of 640.0 nm. Calculate the frequency of this radiation.

Example 2: The YFM radio station broadcasts EM radiation at 99.2 MHz. Calculate the wavelength of this radiation (1 MHz = 106 s-1).

Chapter 6

Quantized Energy and Photons 640.0 nm. Calculate the frequency of this radiation.

- Planck: energy can only be absorbed or released from atoms in fixed amounts called quanta.
- For 1 photon (energy packet):
- E = hf = hc/λ
- where h is Planck’s constant (6.63 10-34 J.s).

Chapter 6

The Photoelectric Effect and Photons 640.0 nm. Calculate the frequency of this radiation.

- If light shines on the surface of a metal, there is a point (threshold frequency) at which electrons are ejected from the metal.

Chapter 6

Example 3: (a) A laser emits light with a frequency of 4.69 x 1014s-1. What is the energy of one photon of the radiation from this laser? If the laser emits a pulse of energy containing 5.0 x 1017 photons of this radiation, what is the total energy of that pulse?

Chapter 6

Line Spectra and the Bohr Model x 10

- Line Spectra
- Monochromatic light – one λ.
- Continuous light – different λs.
- White light can be separated into a continuous spectrum of colors.

Chapter 6

- Balmer: x 10 discovered that the lines in the visible line spectrum of hydrogen fit a simple equation.
- Later Rydberg generalized Balmer’s equation to:
- where RHis the Rydberg constant (1.096776 107 m-1), h is Planck’s constant, n1 and n2 are integers (n2 > n1).

Chapter 6

Bohr Model explains this equation x 10

- Rutherford assumed the electrons orbited the nucleus analogous to planets around the sun.
- However, a charged particle moving in a circular path should lose energy, ie, the atom is unstable
- Bohr noted the line spectra of certain elements and assumed the electrons were confined to specific energy states called orbits.

Chapter 6

Colors from excited gases arise because

electrons move between energy states in the

atom.

Black regions show λs absent in the light

Chapter 6

- Bohr Model because
- Energy states are quantized, light emitted from excited atoms is quantized and appear as line spectra.
- Bohr showed that
- where n is the principal quantum number (i.e., n = 1, 2, 3).

Chapter 6

- The first orbit has becausen = 1, is closest to the nucleus, and has negative energy by convention.
- The furthest orbit has n close to infinity and corresponds to zero energy.
- Electrons in the Bohr model can only move between orbits by absorbing and emitting energy
- ∆E = Efinal – Einitial = hf

Chapter 6

- We can show that because
- When ni > nf, energy is emitted.
- When nf > ni, energy is absorbed

f

Chapter 6

- Limitations of the Bohr Model because
- Can only explain the line spectrum of hydrogen adequately.
- Electrons are not completely described as small particles.

Chapter 6

The Wave Behavior of Matter because

- Explores the wave-like and particle-like nature of matter.
- Using Einstein’s and Planck’s equations, de Broglie showed:
- The momentum, mv, is a particle property, whereas is a wave property.

Chapter 6

The Uncertainty Principle because

- Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously.
- For electrons: we cannot determine their momentum and position simultaneously.
- If Dx is the uncertainty in position and Dmv is the uncertainty in momentum, then

Chapter 6

Quantum Mechanics and Atomic Orbitals because

- Schrödinger proposed an equation that contains both wave and particle terms.
- Solving the equation leads to wave functions, ψ (orbitals).
- ψ2 gives the probability of finding the electron
- Orbital in the quantum model is different from Bohr’s orbit

Chapter 6

Chapter 6 because

- Schrödinger’s 3 QNs: because
- Principal Quantum Number, n. - same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus.

Chapter 6

- Azimuthal Quantum Number, l. - becausedepends on the value of n. The values of l begin at 0 and increase to (n - 1). The letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals.
- Magnetic Quantum Number, ml. - depends on l. Has integral values between -l and +l. Gives the 3D orientation of each orbital. There are (2l +1) allowed values of ml and this gives the no. of orbitals.
- Total no. of orbitals in a shell = n2

Chapter 6

Chapter 6 because

- Orbitals can be ranked in terms of energy to yield an becauseAufbau diagram.

Chapter 6

Single electron atom – orbitals with the same value of n have the same energy

Chapter 6

Representations of Orbitals have the same energy

- The s-Orbitals
- All s-orbitals are spherical.
- As n increases, the s-orbitals get larger & no. of nodes increase.
- A node is a region in space where the probability of finding an electron is zero, 2 = 0.
- For an s-orbital, the number of nodes is (n - 1).

Chapter 6

- The p-Orbitals have the same energy
- There are three p-orbitals px, py, and pz.
- The letters correspond to allowed values of ml of -1, 0, and +1.
- The orbitals are dumbbell shaped and have a node at the nucleus.
- As n increases, the p-orbitals get larger.

Chapter 6

Chapter 6 have the same energy

- The d and f-Orbitals have the same energy
- There are five d and seven f-orbitals.
- They differ in their orientation in the x, y,z plane

Chapter 6

Many-Electron Atoms have the same energy

- Orbitals and Their Energies
- Orbitals of the same energy are said to be degenerate.
- For n 2, the s- and p-orbitals are no longer degenerate because the electrons interact with each other.
- Therefore, the Aufbau diagram looks different for many-electron systems.

Chapter 6

Many electron atoms – electrons repel and thus orbitals are at different energies

- Electron Spin and the Pauli Exclusion Principle are at different energies
- Line spectra of many electron atoms show each line as a closely spaced pair of lines.
- Stern and Gerlach designed an experiment to determine why.

Chapter 6

2 opposite directions of spin produce oppositely directed magnetic fields leading to the splitting of spectral lines into closely spaced spectra

- Since electron spin is quantized, we define magnetic fields leading to the splitting of spectral lines into closely spaced spectrams = spin quantum number = + ½ and - ½ .
- Pauli’s Exclusion Principle: no two electrons can have the same set of 4 quantum numbers.
- Therefore, two electrons in the same orbital must have opposite spins.

Chapter 6

- In the presence of a magnetic field, we can lift the degeneracy of the electrons.

Chapter 6

Electron Configurations degeneracy of the electrons.

- Hund’s Rule
- Electron configurations - in which orbitals the electrons for an element are located.
- For degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron.

Chapter 6

- Condensed Electron Configurations degeneracy of the electrons.
- Neon completes the 2p subshell.
- Sodium marks the beginning of a new row.
- Na: [Ne] 3s1
- Core electrons: electrons in [Noble Gas].
- Valence electrons: electrons outside of [Noble Gas].

Chapter 6

- Transition Metals degeneracy of the electrons.
- After Ar the d orbitals begin to fill.
- After the 3d orbitals are full, the 4p orbitals begin to fill.
- Transition metals: elements in which the d electrons are the valence electrons.

Chapter 6

- Lanthanides and Actinides degeneracy of the electrons.
- From Ce onwards the 4f orbitals begin to fill.
- Note: La: [Xe]6s25d14f0
- Elements Ce - Lu have the 4f orbitals filled and are called lanthanides or rare earth elements.
- Elements Th - Lr have the 5f orbitals filled and are called actinides.
- Most actinides are not found in nature.

Chapter 6

Electron Configurations and the Periodic Table degeneracy of the electrons.

- The periodic table can be used as a guide for electron configurations.
- The period number is the value of n.
- Groups 1A and 2A have the s-orbital filled.
- Groups 3A - 8A have the p-orbital filled.
- Groups 3B - 2B have the d-orbital filled.
- The lanthanides and actinides have the f-orbital filled.

Chapter 6

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