Module 3 Lesson 1: The Bohr Model and Atomic Spectra

Historical Development of Atomic Models

The development of the modern atomic model is a progression of theories built on physics and experimental evidence spanning thousands of years.

• Democritus: He originally proposed that matter is composed of indivisible units called atoms. This idea remained largely ignored for millennia.
• John Dalton (Early 1800s): Dalton reintroduced the concept of the atom, conceptualizing them as small, solid, wooden-ball-like structures.
• J.J. Thomson (1897): Discovered the electron. He proposed a model where electrons were floating freely within a "sea" of positive charge.
• Ernest Rutherford (1912): Discovered the nucleus. He identified that the positive charge is concentrated in the center of the atom and proposed that electrons move around this nucleus in random orbits.
• Niels Bohr: Hypothesized that electrons do not move randomly but occupy specific orbits at fixed distances from the nucleus. This theory was heavily influenced by the study of light and electromagnetic radiation.

Characteristics of Electromagnetic Radiation

Electromagnetic radiation is a form of energy that travels through space exhibiting wave-like behaviors. Understanding the Bohr model requires understanding the properties of these waves.

• Wavelength ($\lambda$): The distance between corresponding points on adjacent waves (e.g., from one peak to the next).
  • Long wavelengths are associated with low frequency.
  • Short wavelengths are associated with high frequency.
• Frequency ($f$ or $\nu$): The number of waves that pass a specific point in a given amount of time.
• Inverse Relationship: Wavelength and frequency are inversely proportional. As wavelength increases, frequency decreases.
• The Electromagnetic Spectrum: Organized by energy, frequency, and wavelength.
  • Gamma Rays: Highest energy, highest frequency, shortest wavelength.
  • X-rays: High energy.
  • Ultraviolet (UV): High energy radiation.
  • Visible Light: The narrow range of the spectrum detectable by the human eye.
  • Infrared (IR): Lower energy than visible light.
  • Microwave: Low energy.
  • Radio Waves: Lowest energy, lowest frequency, longest wavelength.

Unit Conversions and Reference Materials

In chemistry reference tables (specifically Page 8), the Bohr model and emission spectra are analyzed using specific units of distance.

• Equality for Conversion: $1\,m = 10^9\,nm$ (one meter equals one billion nanometers).
• Conversion Formula: To convert meters to nanometers, use the starting value and multiply by a conversion factor: $\frac{10^9\,nm}{1\,m}$.
• Example 1: Converting $7.0 \times 10^{-7}\,m$ to nanometers.
  • $7.0 \times 10^{-7}\,m \times \frac{10^9\,nm}{1\,m} = 7.0 \times 10^{2}\,nm = 700\,nm$ (Moving the decimal two places to the right).
• Example 2: Converting $6.5 \times 10^{-7}\,m$ to nanometers.
  • $6.5 \times 10^{-7}\,m \times \frac{10^9\,nm}{1\,m} = 6.5 \times 10^{2}\,nm = 650\,nm$.

The Photoelectric Effect

This experiment was foundational in establishing that light behaves as a particle in addition to behaving as a wave.

• Observation: Light shining on a metal surface can eject electrons.
• Frequency vs. Intensity:
  • Low-frequency light (long wavelength) will never eject an electron, regardless of how bright (intense) the light is.
  • High-frequency light will eject an electron even if the intensity is very low.
• Threshold (Minimum Frequency): There is a specific minimum frequency required to dislodge an electron, which varies depending on the metal used.
• Electron Speed: Once the threshold is passed, the speed of the ejected electron is determined by the light's frequency, not its intensity.
• Albert Einstein's Contribution: He identified light as consisting of discrete particles called photons.
  • Photons have zero mass.
  • Quantum: The discrete amount of energy carried by a photon. This energy is directly proportional to frequency.

Hydrogen Emission Spectrum and Bohr’s Hypotheses

Bohr used the light emitted by hydrogen atoms to map the structure of the atom.

• The Experiment:
  1. Electricity is passed through a tube of hydrogen gas, creating "excited" atoms.
  2. As atoms return to their "ground state," they emit electromagnetic radiation.
  3. This radiation passes through a series of slits and a prism.
  4. The prism separates the light into a line emission spectrum.
• Line vs. Continuous Spectra: Unlike a continuous rainbow, the line emission spectrum only shows specific wavelengths specific to the element.
• Atomic Fingerprint: Every element has its own distinct spectrum; Bohr used these specific lines as evidence against random electron orbits.
• Bohr’s Proposals:
  • Orbits: Electrons exist in specific circular paths (orbits) at fixed distances from the nucleus.
  • Exclusion: Electrons cannot exist in the space between these orbits.
  • Energy Levels ($n$): Each orbit is an energy level. The level closest to the nucleus is $n=1$.
  • Energy Gradients: Outer orbits ($n=2, 3, etc.$) have higher energy than inner orbits. Gaps between energy levels are largest near the nucleus ($n=1$ to $n=2$) and get progressively smaller as the levels move outward.
  • States of Matter:
    • Excited State: An electron absorbs a quantum of energy and jumps to a higher energy level.
    • Ground State: When an electron drops back to its original level, it releases energy as electromagnetic radiation.
  • The Ladder Metaphor: Just as a person can stand on the steps of a ladder but not on the empty space between them, electrons can only occupy specific energy rungs.

Interpreting the Hydrogen Spectrum Diagram

Using the Bohr model diagram, specific electron transitions can be linked to specific wavelengths of light.

• Transition Calculation: The energy released when an electron drops levels corresponds exactly to the energy of the emitted photon.
• Practice Problem 1: Move from $n=6$ to $n=3$.
  • Tracing the line on the reference table leads to an emission of $1094\,nm$.
• Practice Problem 2: Move from $n=3$ to $n=2$.
  • Tracing the line leads to a wavelength of $656\,nm$.
  • Referencing the visible spectrum (which spans $400\,nm$ to $700\,nm$), a wavelength of $656\,nm$ falls in the red light range.
• Practice Problem 3: Emitted light is $1875\,nm$.
  • Working backward on the diagram, this wavelength corresponds to an electron moving from $n=4$ to $n=3$.
• Practice Problem 4: Move from $n=2$ to $n=1$.
  • This transition releases light at a wavelength of $122\,nm$.
  • Referencing the EM spectrum, this falls into the Ultraviolet (UV) range.

Limitations of the Bohr Model and Subsequent Theories

Despite its breakthroughs, the Bohr model was eventually refined due to inherent limitations.

• Element Complexity: The Bohr model only successfully explained the line spectrum for Hydrogen ($H$). For heavier elements, the spectral lines appear as doublets or triplets, which the model could not explain.
• Heisenberg Principle of Uncertainty: Bohr’s model assumes we can determine the electron’s exact location and momentum (speed) simultaneously. Werner Heisenberg later proved it is impossible to know both at the same time.
• Later Contributors:
  • Louis de Broglie: Proposed that moving particles, such as electrons, possess wave-like properties.
  • Erwin Schrödinger: Developed mathematical equations to describe the probabilistic location of electrons, leading to the current Quantum Mechanical Model.