SUMMARY
The de Broglie wavelength of a 5.0 eV electron can be calculated using the formula λ = h/p, where p is the momentum derived from the kinetic energy equation E = p²/(2m). The correct momentum for a 5.0 eV electron is calculated as p = √(2mE), resulting in a wavelength of approximately 5.48 x 10-10 m after converting energy from electron volts to joules. A common mistake is neglecting to include the factor of 2 in the kinetic energy formula and failing to convert eV to joules, which leads to incorrect wavelength calculations.
PREREQUISITES
- Understanding of quantum mechanics concepts, specifically de Broglie wavelength.
- Familiarity with the relationship between energy, momentum, and mass.
- Knowledge of unit conversions, particularly between electron volts and joules.
- Basic proficiency in algebra and solving equations.
NEXT STEPS
- Study the derivation of the de Broglie wavelength formula.
- Learn about the conversion of electron volts to joules and its significance in calculations.
- Explore kinetic energy equations for particles at relativistic speeds.
- Investigate the implications of potential difference on electron acceleration and energy.
USEFUL FOR
Students and professionals in physics, particularly those studying quantum mechanics, as well as educators looking to clarify concepts related to electron behavior and wave-particle duality.
