03 CHEM 1201 - Bohr's Model of the Atom

Describe Bohr’s theory of the hydrogen atom
Define and correctly use the terms:
- Excitation: the process when an electron absorbs energy and moves to a higher energy level.
- Relaxation: when an electron loses energy and drops to a lower energy level.
- Absorption: the process in which an electron absorbs energy from an incoming photon.
- Emission: when an electron emits energy in the form of a photon as it transitions to a lower energy state.
Sketch an energy level diagram for the hydrogen atom.
Calculate the energy for an electronic transition within the hydrogen atom.

Two main processes to analyze electron structures:
1. Add energy to vaporize a sample to examine emitted light.
2. Shine a full spectrum of light at a vaporized sample to observe light absorption.

Continuous Spectrum:
- Emission spectrum of white light or sunlight; contains all wavelengths of light.
- Represents the visible spectrum of sunlight.
Line Spectra:
- Emission spectra of atoms produce narrow colored lines, each corresponding to specific wavelengths (λ) of light, which relate to definite energy levels.
- Examples:
  - Hydrogen Emission Spectrum
  - Hydrogen Absorption Spectrum

Observation of few wavelengths (λ or ν) indicates limited energy transitions for elements.
The energy of an electron is quantized; electrons are bound to specific energy levels.

Illustrates nad transitions between orbits:
- Lower-energy orbits and Higher-energy orbits.
- Transition examples include from n=4 and n=3 down to n=1 and n=2.

Sketch an energy-level diagram with all excitation paths terminating at n_final = 6.
Identify the highest energy transition and the longest wavelength transition from the diagram.

Involves energy transfer between electrons and photons.
Absorption Spectra: Light shines through a vaporized element, leading to the absorption of specific wavelengths.
Emission Spectra: Transitions from a high energy state to a lower energy state leading to emitted light.

Diagram indicating H₂ emission (top) and absorption (bottom) spectra across wavelengths (400-700 nm).

Johann Balmer derived the mathematical formula fitting observed wavelengths of H₂ in the visible region (n = 3, 4, 5, 6).
- Formula:[
  u = constant \cdot \left( \frac{1}{n^2} - \frac{1}{2^2} \right) ]

Rydberg expanded on Balmer’s findings with a broader formula applicable to visible, ultraviolet, and infrared regions.
- Rydberg formula relates wavelength to energy level transitions:[ \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) ], with n_1, n_2 as positive integers (n_2 > n_1).

Required a singular assumption: electrons orbit the nucleus in circular paths (orbits) with specific allowed radii.

Represents hydrogen orbits at different energy levels: n=1 through n=6, demonstrating distance from the nucleus.

Covers transitions classified into series:
- Lyman Series: transitions to n=1 (UV).
- Balmer Series: transitions to n=2 (Visible).
- Paschen Series: transitions to n=3 (IR).

Electron energy in orbits is defined by principal quantum number (n), an integer (1, 2, 3...).

Energy for transitions calculated by:[ \Delta E = E_{final} - E_{initial} = -R_{hc} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) ]

An electron transitions from n=7 and emits a photon of 1006 nm. Steps:a) Calculate the emitted photon's energy.b) Find the change in energy of the electron.c) Determine the new final state (n_final).

Electrons occupy specific orbits, with proximity to the nucleus indicating energy levels.
Observed wavelengths were predicted effectively by the model.
The model successfully explained spectral lines across various series and applied well to one-electron systems.