CHMA10 - Quantum Mechanical Model of the Atom

Quantum Mechanical Model Overview

• The Quantum Mechanical Model of the Atom replaces earlier models, incorporating new scientific ideas from the 20th century.

The Solvay Conference, 1927

• Major scientific figures gathered to discuss groundbreaking concepts in quantum mechanics.

Nature of Light

• In 1873, Maxwell proposed that visible light consists of electromagnetic waves composed of oscillating electric and magnetic fields.
• Light behavior can be described using amplitude, wavelength (λ), and frequency (ν) with the equation:
  ( \nu = \frac{c}{\lambda} ) where ( c = 3 \times 10^8 m/s ) (speed of light).

Electromagnetic Radiation

• Defined as energy emitted and transmitted in electromagnetic waves.
• Consists of a spectrum that includes various types of radiation.

Wave Interference

• Constructive interference occurs when waves are in phase, enhancing amplitude.
• Destructive interference occurs when waves are out of phase, reducing amplitude.

Diffraction of Waves

• Diffraction refers to the bending of waves around obstacles or openings, evidence of wave properties.
• Light shows diffraction patterns when passing through narrow openings.

Evidence Supporting Wave Theory

• The double-slit experiment demonstrates the wave nature of light through interference patterns of light and dark spots.

Blackbody Radiation

• A blackbody absorbs all radiation and re-emits it across a broad range of frequencies, with intensity varying by frequency.
• As temperature increases, the emitted frequency shifts towards the visible spectrum.

Ultraviolet Catastrophe

• Classical physics fails to predict blackbody radiation at short wavelengths, leading to the UV catastrophe.
• Proposed solutions required quantum mechanics to explain deviations.

Photoelectric Effect

• Observes that light below a threshold frequency ( \nu_0 ) does not eject electrons.
• Higher frequency light results in higher kinetic energy of ejected electrons, but doesn’t affect the ejection rate.

Amplitude and Electron Ejection

• Higher amplitude light results in more electrons being ejected per unit time but does not impact their kinetic energy.

Quantum Mechanics and Photons

• Einstein proposed that light exists as discrete packets called photons, winning the Nobel Prize for explaining the photoelectric effect.
• The energy of a photon is given by ( E_{photon} = h\nu = \frac{hc}{\lambda} ).

Threshold Frequency Explained

• A photon must have minimum energy to eject an electron, explaining the threshold frequency; photons below this value cannot eject electrons.

Example Calculation of Photon Energy

• For microwave radiation with a wavelength of 1.20 cm, the energy of one photon can be calculated using:
  ( E = \frac{hc}{\lambda} ), substituting known values leads to the energy outcome.

Learning Goals for Quantum Mechanics

• Recognize the need for quantum mechanics and key figures involved in its development.
• Relate energy of light quanta to their frequency and wavelength.
• Interpret atomic emission spectra through Bohr's atomic theory and calculate energy changes for emissions.