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Key Equations of Atomic Theory
Oct 19, 2024
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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.
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Full transcript
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.