SUMMARY
The shortest wavelength photon emitted in a hydrogen atom corresponds to the transition of an electron from the n=2 energy level to the n=1 energy level, resulting in an energy change of 10.2 eV. The formula used to calculate the wavelength is λ = hc/E, where h is Planck's constant (4.14 x 10^-15 eV*s) and c is the speed of light (3.00 x 10^8 m/s). The correct calculation yields a wavelength of approximately 9.73 x 10^-8 m. The initial misunderstanding involved using -13.6 eV instead of the positive energy change associated with the transition.
PREREQUISITES
- Understanding of quantum mechanics and energy levels in atoms
- Familiarity with the hydrogen atom's energy levels
- Knowledge of Planck's constant and the speed of light
- Ability to manipulate equations involving energy and wavelength
NEXT STEPS
- Study the hydrogen spectral series and its implications for photon emission
- Learn about energy transitions in other elements and their spectral lines
- Explore the concept of photon energy and its relationship to wavelength
- Investigate the role of quantum mechanics in atomic structure and electron transitions
USEFUL FOR
Students studying quantum mechanics, physics educators, and anyone interested in atomic theory and photon behavior in hydrogen atoms.