Chemistry Chapter on Periodic Table and Elements

Unit 3 - Electrons in Atoms

• Unit covers electrons in atoms, light, blackbody radiation, photoelectric effect, hydrogen atom, quantum mechanics, periodic table and electron configurations.

3.0 Unit Coverage

• Topics include light, blackbody radiation, photoelectric effect, hydrogen atom, quantum mechanics, periodic table and electron configurations.

3.1 Introduction To Light

• Light is an electromagnetic wave carrying energy.
• Different colors (e.g., red, blue) correspond to different wavelengths (e.g., longer, shorter) and frequencies.
• 480 THz, 635 nm
• 510 THz, 590 nm
• 540 THz, 560 nm
• 610 THz, 490 nm
• 670 THz, 450 nm
• 750 THz, 400 nm

3.1 Electromagnetic Spectrum

• Light is an electromagnetic wave carrying energy.
• Different colors correspond to different wavelengths and frequencies.
• The spectrum includes gamma rays, X-rays, ultraviolet, visible, infrared, microwaves, and radio waves.
• The energy of light is inversely proportional to its wavelength.

3.1 Characterization Of Waves

• Frequency (v): number of peaks passing a point per unit time (measured in Hz, where 1 Hz = 1 s⁻¹).
• Wavelength (λ): distance between peaks (measured in meters). Nanometers (nm) are frequently used for visible light (1 nm = 10⁻⁹ m).

3.1 Speed Of Waves

• The speed of light (c) is constant (approximately 2.9979 × 10⁸ m/s).
• Wavelength (λ) is equal to the speed of light (c) divided by the frequency (v): λ = c/v

3.1 Electromagnetic Spectrum Revisited

• Frequency and wavelength of light are inversely proportional.
• The energy of light is proportional to frequency (E = hv), where h is Planck's constant.

3.2 Blackbody Radiation

• All objects emit electromagnetic radiation due to thermal energy.
• The radiation's intensity pattern depends on its temperature.

3.2 Ultraviolet Catastrophe

• Classical wave theory failed to explain observed blackbody spectra at short wavelengths (ultraviolet catastrophe).

3.2 Max Planck and Quantization

• Planck proposed that light energy is quantized, meaning it comes in discrete packets called photons.
• The energy of a photon (Ephoton) is related to its frequency (ν) by Ephoton = hν, where h is Planck's constant (6.62606957×10⁻³⁴ Js).

3.3 Photoelectric Effect

• Light striking a metal surface can eject electrons.
• The emission of electrons depends on the frequency of light and not its intensity.
• The maximum kinetic energy of emitted electrons depends linearly on the frequency of the incident light, once the threshold frequency (minimum frequency for emission) is exceeded.

3.3 Work Function

• The threshold frequency (ν₀) is related the work function (Φ) by Φ=hν₀.
• The relationship between the kinetic energy of the ejected electron (Ek), the incident light frequency (ν), and the work function (Φ) of the metal is Ek = hν − Φ.

3.3 Example - Threshold Frequency

• The threshold frequency for calcium (given its work function) can be calculated using the equation ν= Φ/(h).

3.3 Example - Kinetic Energy

• The kinetic energy of an ejected electron from calcium (for a given wavelength) is calculated using the formula Ekin = hv − Φ.

3.4 Emission Spectra of Elements

• Each element produces a unique emission spectrum.

3.4 Discrete Energy Levels

• Atoms have discrete energy levels, meaning electrons can only exist at specific energy levels.
• Transitions between energy levels involve absorbing or releasing energy in the form of photons.

3.4 Hydrogen Atom

• The hydrogen atom has a simple set of energy levels.
• The energy level of hydrogen is given by the formula Eₙ = -Rᵢₑ/n² where n is an integer (1, 2, 3…); Rᵢₑ is equal to a constant that depends on the mass of the fundamental particles (electron, proton, etc.).

3.4 Energy of Electron Transition

• Electron transitions between energy levels involve absorbing or emitting a photon with energy ΔE related to the energy levels via ΔE = ±hν.

3.4 Hydrogen Atom Examples

• Calculate the frequency of emission lines when a hydrogen atom transitions.

3.5 Wave Functions

• The solutions to Schrödinger's equation describe the state of an electron in an atom as a wave.
• Ψ² gives the probability of finding an electron at a particular location.

3.5 Principal Quantum Number

• The principal quantum number (n) describes the energy and distance of an electron from the nucleus.

3.5 Angular Momentum Number

• The angular momentum quantum number (l) describes the shape of an electron's orbital.

3.5 Magnetic Quantum Number

• The magnetic quantum number (ml) describes the orientation of an electron's orbital in space.

3.5 s Orbitals

• s orbitals have a spherical shape.
• The number of nodal spheres is n - 1, where n is the principal quantum number.

3.5 p Orbitals

• p orbitals have a dumbbell shape.
• A nodal plane separates the two lobes.
• There are three degenerate p orbitals (mₗ = -1, 0, +1).

3.5 d Orbitals

• d orbitals have a more complex cloverleaf shape.
• There are five degenerate d orbitals (mₗ = -2, -1, 0, +1, +2).

3.5 Specifying Orbitals

• The combination of the n, l, and mₗ designations specify an orbital.
• This corresponds to an electron's motion around the nucleus.

3.5 Spin Quantum Number

• Electrons exhibit spin, a property described by the spin quantum number with possible values of +½ or -½.
• There are two states associated with the lowest energy level.

3.5 Hydrogen Energy Levels

• The energy levels are related to the principal quantum number (n) by Eₙ = -Rᵢₑ/n², where Rᵢₑ is the Rydberg constant.
• The number of orbitals associated with a given energy level is equal to n².

3.5 Orbitals and States of Hydrogen

• Provides a table relating the values of n, l, the number of orbitals, and the total number of states, or electrons, for each energy level.

3.6 One Electron Systems

• Ions with a single electron have the same orbitals as hydrogen, modified by the nuclear charge.

3.6 Multielectron Systems

• Calculating energy levels is complicated by electron repulsions.
• The Pauli Exclusion Principle dictates that no two electrons can have the same set of quantum numbers.
• Electrons fill orbitals in order of increasing energy to minimize their mutual repulsion.

3.6 Ground State Electron Configurations

• Aufbau's Principle: Electron configurations are determined by filling orbitals in order of increasing energy.

3.6 Electron Configuration Exceptions

• In some elements, notably Cr and Cu, electron configuration exceptions occur because of the stabilization gained from particular half-filled and fully-filled subshells.

3.6 Diamagnetic vs Paramagnetic

• A paramagnetic material has unpaired electrons, which align with external magnetic fields, making the material attracted to the field; diamagnetic materials do not have unpaired electrons and thus are repelled by the field.

3.6 Periodic Table Blocks

• The s, p, d, and f blocks of the periodic table correspond to the filling of different types of electron orbitals.

3.6 Development of the Periodic Table

• Describes the historical progression of organizing elements into a periodic table. Key contributors and their contributions are noted.

Additional Topics

• 3.5 Radial Probability Distributions: Visualizes the probability of finding an electron at various distances from the nucleus.
• Spotlight in Engineering-Electron Corral: Describes an experiment demonstrating the wave-like nature of electrons.
• Additional examples of electron configurations: Provides specific examples of writing electron configurations for various elements and ions.