Atomic and Molecular physics pp p TTT B
- 1. PRESENTATION PHYSICS Schrondinger’s Equation For Hydrogen Atom
- 2. Historical Background •The Schrodinger equation, was developed by Erwin Schrodinger in 1926.Schrodinger's work on wave mechanics, including the Schrödinger equation, earned him the Nobel Prize in Physics in 1933.Schrodinger successfully applied his equation to the hydrogen atom, predicting its spectral lines and other properties, .
- 3. What is Schrondinger’s Equation ? The Schrodinger equation is a mathematical expression that describes the energy and position of an electron in space and time while accounting for the electron’s matter wave nature inside an atom.
- 5. The position of a particle is distributed through space like the amplitude of a wave . In quantum mechanics, a wavefunction describes the motion and location of a particle . Symbols used: ψ (psi). • A wavefunction is just a mathematical function which may be large in one region, small in others, and zero elsewhere.
- 6. Derivation of the Schrodinger Equation •Waves are classified into two kinds: •a. Standing waves. b. Progressive waves To derive the Schrödinger equation, we use standing wave equations because they provide a better description of the motion of electrons in their orbit around the nucleus.An important property of light is that it obeys the following differential equation for standing waves: ∂²φ/∂x² = (1/v²) ∂²φ/∂t²
- 7. Where φ is defined as: φ = 2r sin(2πx/λ) cos(2πvt) In these two equations: t is the time V is the speed of light λ is the wavelengthν (often v, in practice) is the frequency x is the displacementr is the amplitude of the standing wave
- 8. Applications of Schrodinger equation The Schrodinger equation for the hydrogen atom is a foundational result in quantum mechanics with several important uses and applications in physics, chemistry, and related fields
- 9. •1. Determination of Energy Levels: Solving the time-independent Schrodinger equation for hydrogen gives quantized energy levels. These levels explain the hydrogen atomic spectrum (e.g., Balmer, Lyman series).
- 10. •2. Atomic Orbital Shapes The solution provides wavefunctions (orbitals) that describe the probability distribution of the electron . These give rise to the familiar s, p, d, f orbitals, important in understanding chemical bonding and molecular structure.
- 11. •3. Spectroscopy It underpins atomic absorption and emission spectra . Predicts spectral lines with great accuracy and explains fine structure with relativistic corrections.
- 12. •4. Quantum Numbers • Derivation of quantum numbers (n, l, m) helps define • Electron configurations
- 13. THANKS