Lecture on Bohr Model and Energy Levels of Hydrogen

Introduction

• Previous video derived an equation using physics principles (not necessary for this video).
• Focus: energy levels of electrons in a hydrogen atom using the Bohr model.

Energy Levels and Conversion

• E₁: Energy for lowest level electron in hydrogen (Bohr model)
  • Calculated as (-2.17 \times 10^{-18}) joules.
  • Convert to electron volts:
    • 1 electron volt = (1.6 \times 10^{-19}) joules.
    • Energy in electron volts: (-13.6) eV for n=1.

Energy Level Calculation Formula

• Energy at level n: (E_n = \frac{E_1}{n^2})
• Examples:
  • n=1: (-13.6) eV
  • n=2: (-3.4) eV
  • n=3: (-1.51) eV

Bohr Model Overview

• Electrons orbit a positively charged nucleus.
• Energy and radius quantized: cannot have intermediate values.
• Higher n corresponds to higher (less negative) energy.

Energy Transitions

• Energy differences dictate electron transitions between levels.
• Example Transitions:
  • n=1 to n=2: Requires 10.2 eV.
  • n=1 to n=3: Requires 12.09 eV.
  • Ionization (n=1 to infinity): Requires 13.6 eV.

Ionization and Potential Energy

• Ionization happens when the electron is infinitely away from the nucleus (zero total energy).
• Energy required to ionize (remove electron) from hydrogen is 13.6 eV.
• This matches predicted ionization energy for hydrogen in Bohr model.

Conclusion

• The Bohr model predicts quantized energy levels and ionization energy accurately for hydrogen.
• Useful in understanding atomic structure despite not being to scale.