Lecture Notes: Electronic Transitions and the Bohr Model

Introduction

• Topic: Electronic Transitions (absorption and emission)
• Focus: Bohr model of the atom
• Goals:
  • Understand what the Bohr model got right and wrong
  • Calculate the energy of electronic transitions
  • Explore emission line spectra as a fingerprint for atoms
  • Discuss Lyman, Balmer, Paskin, Brackett series
• Presenter: Chad from Chad's Prep
• Courses offered: High school and college science prep, MCAT, DAT, OAT

Bohr Model of the Atom

• Works well for the hydrogen atom but not for multi-electron systems
• Key Points:
  • Electrons orbit the nucleus in fixed orbits with set energies
  • Potential energy decreases as electron gets closer to the nucleus
  • Energy of an electron in an orbit:
    • Formula: (E = -2.18 \times 10^{-18} \text{J} / n^2)
    • (n) denotes orbit number (n=1, 2, 3,...)
    • Energy becomes less negative with higher orbits

Electronic Transitions

• Electrons absorb or emit photons to move between orbits
• Absorption:
  • Electron moves to a higher orbit by absorbing specific energy from a photon
• Emission:
  • Electron falls to a lower orbit and emits a photon
• Energy difference (\Delta E) calculation:
  • (E_{photon} = E_{final} - E_{initial})
  • Photon energy ((E = h\nu) or (E = \frac{hc}{\lambda}))_

Emission Line Spectra

• Emission spectra provide unique fingerprints for atoms
• Used to identify elements in stars and sun
• Absorption spectra: Certain wavelengths absorbed, causing missing colors

Series in Emission Spectra

• Lyman Series: Electrons fall to (n=1)
  • Ultraviolet region
• Balmer Series: Electrons fall to (n=2)
  • Visible spectrum, most important
• Paskin Series: Electrons fall to (n=3)
  • Infrared region
• Brackett Series: Electrons fall to (n=4)
  • Infrared region

Calculations

• Energy of an electron in an orbit or transition calculated using Bohr's formula
• Wavelength or frequency of emitted or absorbed photons can be found using known constants (Planck's constant, speed of light)
• Rydberg Equation for direct wavelength calculation

Conclusion

• Importance of Bohr model in understanding atomic structure
• Use of spectra in determining composition of celestial bodies
• Encouragement to use further resources for study and practice

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