Atomic Models and Quantum Mechanics

Bohr's Model

• Bohr proposed that electrons jump to specific energy levels, like rungs on a ladder, particularly for hydrogen.

• The observation of only four wavelengths for hydrogen suggested discrete energy levels rather than a continuous range.

• Electrons can only absorb specific amounts of energy to move to higher energy levels. If the energy is insufficient, the electron remains at its current level.

• Analogy: Giving 10 units of energy allows an electron to jump to a level requiring 10 units. Giving 5 units results in no movement.

Quantized Energy

• Energy is quantized, meaning it comes in discrete amounts.

• Electromagnetic radiation (light) exhibits particle-like behavior as photons, each with a specific amount of energy.

• Equation for the energy of a photon: $E = h \nu$, where:

  • $E$ is the energy of the photon.

  • $h$ is Planck's constant.

  • $\nu$ is the frequency.

• Alternative formula: $E = \frac{hc}{\lambda}$, where:

  • $c$ is the speed of light.

  • $\lambda$ is the wavelength in meters.

Units and Constants

• Planck's constant (h) has units of joule-seconds (J⋅s).

• The speed of light (c) is approximately $3.0 \times 10^8$ meters per second (m/s).

• Wavelength ($\lambda$) must be in meters.

• Energy is measured in Joules.

Applying the Equations

• The equations are tools to be used based on the available information (frequency or wavelength).

• Photons have discrete amounts of energy, which are multiples of Planck's constant times frequency ($h\nu$).

Energy Transfer

• Energy can only be gained or lost in integer multiples of $h\nu$, representing specific amounts of energy.

• A system transfers a whole quantum or packet of energy.

• Analogy: Like rungs on a ladder, you can only step on existing rungs, requiring a specific amount of energy to reach each rung.

Wave-Particle Duality

• Electromagnetic radiation (light) exhibits both wave-like and particle-like properties.

• Light behaves as both a wave and discrete particles with specific energy.

Example Calculation

• Calculating the energy of a radio wave with a wavelength of $1.3 \times 10^4$ meters:

  • $E = \frac{hc}{\lambda}$

  • $E = \frac{(6.626 \times 10^{-34} \text{ J⋅s}) \times (3.0 \times 10^8 \text{ m/s})}{1.3 \times 10^4 \text{ m}}$

  • $E \approx 1.5 \times 10^{-29} \text{ J}$

• Units cancel out to leave Joules, a unit of energy.

• The result is the energy of a single photon.

Unit Conversions

• Wavelength must be in meters; convert from nanometers if necessary.

• The appropriate equation is selected based on the given units (meters for wavelength, per second for frequency).

Atomic Excitation and Emission

• Atoms can be excited by shining light on them, causing electrons to jump to higher energy levels.

• When electrons drop back down, they emit energy in the form of photons.

• Atoms can be excited using electricity or a flame.

Limitations of Bohr's Model

• Bohr's model postulates discrete quantized energy levels and specific electron orbits.

• Bohr's model breaks down when applied to elements with many electrons.

• The model is a useful, but limited, representation of atomic structure.

• Bohr's model correctly describes elements up to about 10 electrons

Wave Mechanical (Quantum Mechanical) Model

• A newer model is called the wave mechanical model or quantum mechanical model.

• Instead of orbits, it describes orbitals, which are three-dimensional volumes.

• Electrons move within these orbitals, with a higher probability of being found in certain regions.

• Orbits are two-dimensional, while orbitals are three-dimensional volumes where electrons are likely to be found.