Atomic Theory Formulas Review

Key Equations and Concepts

1. Speed of Light (c)

• Formula: ( c = \lambda \nu )
  • ( c ): Speed of light ( (3 \times 10^8 \text{ m/s}) )
  • ( \lambda ): Wavelength
  • ( \nu ): Frequency
• Calculating Wavelength: ( \lambda = \frac{c}{\nu} )
• Calculating Frequency: ( \nu = \frac{c}{\lambda} )

2. Energy of a Photon (E)

• Formula: ( E = h \nu )
  • ( E ): Energy of a photon
  • ( h ): Planck’s constant ( (6.626 \times 10^{-34} \text{ J} \cdot \text{s}) )
• Alternate Formula: ( E = \frac{hc}{\lambda} )
• Conversion: 1 nanometer ( = 1 \times 10^{-9} \text{ m} )

3. Photoelectric Effect

• Kinetic Energy Equation: ( KE = E_{\text{photon}} - \phi )
  • ( \phi ): Work function (threshold energy)
• Photon Energy: ( E_{\text{photon}} = h\nu )
• Threshold Energy: ( \phi = h\nu_0 )
• Using Wavelength: Substitute ( \nu = \frac{c}{\lambda} )
• Max Wavelength for Electron Ejection: ( \lambda_{\text{max}} = \frac{hc}{\phi} )
• Conversion: 1 electron volt ( = 1.62 \times 10^{-19} \text{ J} )

4. De Broglie Wavelength

• Formula: ( \lambda = \frac{h}{mv} )
  • ( m ): Mass of the object
  • ( v ): Velocity of the object
• Momentum: ( p = mv )
• Alternate Momentum Formula: ( p = \frac{h}{\lambda} )

5. Hydrogen Atom Photon Emission

• Energy Emission Formula: ( E = -2.178 \times 10^{-18} \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) )
  • ( n_f ): Final energy level
  • ( n_i ): Initial energy level
• Calculate Frequency: ( \nu = \frac{E}{h} )
• Calculate Wavelength: ( \lambda = \frac{hc}{E} )

Additional Information

• Mass of Electron: ( 9.11 \times 10^{-31} \text{ kg} )
• Mass of Proton: ( 1.6726 \times 10^{-27} \text{ kg} )
• Mass of Neutron: ( 1.6749 \times 10^{-27} \text{ kg} )

Resources

• Formula sheets and additional example problems are available through provided links for deeper understanding and practice.