Unit 3: Atomic Physics
Table of Contents
1. Bohr's Model of the Atom
In 1913, Niels Bohr proposed a model for the Hydrogen atom to explain its line spectrum. He introduced the idea that electrons move in fixed, non-radiating orbits.
Main Postulates:
- Electrons revolve in circular orbits where the angular momentum is quantized: L = n\hbar.
- Electrons do not radiate energy while in these stationary orbits.
- Energy is emitted or absorbed only when an electron jumps from one orbit to another (E2 - E1 = hν).
2. Frank-Hertz Experiment
This experiment provided the first direct evidence for quantized energy levels in atoms. By bombarding Mercury vapor with electrons, they observed that energy was absorbed only in specific discrete amounts.
The periodic drops in current at specific voltages (4.9V for Mercury) confirmed that electrons lose energy only when it matches a specific transition energy of the atom.
3. Sommerfeld's Elliptical Orbits
Arnold Sommerfeld extended Bohr's model by introducing elliptical orbits. This helped explain the "fine structure" of spectral lines.
- Introduced a second quantum number, the Azimuthal quantum number (l).
- Accounted for relativistic mass variations of the electron as it speeds up near the nucleus.
4. Vector Atom Model & Quantum Numbers
The modern description of the atom uses four quantum numbers to define the state of an electron:
| Quantum Number | Symbol | Defines |
|---|---|---|
| Principal | n | Main shell/Energy level (1, 2, 3...) |
| Azimuthal (Orbital) | l | Subshell shape (0 to n-1) |
| Magnetic | ml | Orientation in space (-l to +l) |
| Spin | ms | Direction of spin (+1/2 or -1/2) |
5. Stern-Gerlach Experiment & Electron Spin
This experiment proved the existence of Electron Spin and Space Quantization. By passing a beam of Silver atoms through a non-uniform magnetic field, the beam split into two distinct spots.
Conclusion: The splitting confirmed that electrons have an intrinsic magnetic moment due to spin, which can only have two orientations (up or down).
6. X-ray Spectra and Moseley's Law
When high-speed electrons strike a target, they produce two types of X-rays:
- Continuous X-rays (Bremsstrahlung): Produced by the deceleration of electrons.
- Characteristic X-rays: Produced when an inner-shell electron is ejected and an outer electron falls into its place.
Moseley's Law:
Henry Moseley discovered that the frequency of characteristic X-rays is related to the atomic number (Z).
This law proved that Z (Atomic Number) is more fundamental than atomic weight for organizing the Periodic Table.
Exam Focus Corner
Frequently Asked Questions
- Why did Bohr's model fail for multi-electron atoms? It didn't account for electron-electron repulsions and could not explain the relative intensities of spectral lines.
- What is the physical significance of the Stern-Gerlach experiment? It demonstrated that angular momentum is quantized in space (it can't point in just any direction).
Common Mistakes
- Rydberg Formula: Make sure to distinguish between the wavelength (λ) and the wave number (1/λ).
- Pauli Exclusion Principle: Always remember that no two electrons in an atom can have the same set of four quantum numbers.
Exam Tips
Tip: For the Frank-Hertz experiment, remember that the mean free path of the electron must be large enough to reach the excitation energy, which is why the experiment is conducted at low pressures.