de Broglie Standing Waves in Bohr Orbits
Combining lambda = h/(mv) with 2 pi r_n = n lambda gives m v_n r_n = n hbar. In a Coulomb Bohr atom, the electron wavelength therefore scales as n/Z.
Why this shows up in the exam
Comparing orbital matter wavelengths · Deriving Bohr angular-momentum quantization · Relating orbit circumference to quantum number
Learn the idea
An allowed Bohr orbit fits an integer number of electron de Broglie wavelengths around its circumference. A wave closes smoothly around the orbit only when the circumference contains whole wavelengths. A fractional leftover would return with the wrong phase.
🧠 Memory hook: Whole waves close the orbit.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- 2 pi r_n = n lambda_n — standing-wave condition around a Bohr orbit
- lambda_n = h/(m v_n) — non-relativistic electron de Broglie wavelength
- lambda_n proportional to n/Z — hydrogen-like orbital wavelength scaling
How to approach it
- 1Identify which wavelength the question means
- 2Use circumference equals n wavelengths
- 3Cross-check with L = n hbar
Common slip-ups that cost marks
- •Using lambda = circumference for every n
- •Confusing emitted-photon wavelength with electron wavelength
- •Applying h/(mv) relativistically
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
In hydrogen, an electron transitions from n = 2 to n = 1. Using E_n = -13.6/n^2 eV, find the emitted photon energy.
More from Atoms and Nuclei
Hydrogen spectrum and spectral series
Understand the origin, calculation, and interpretation of spectral lines, series limits, wavelength and frequency relations, and transitions in hydrogen and hydrogen-like ions.
Atomic models and Bohr theory
Learn the historical development of atomic models, especially the Bohr model, and how it explains the structure, radii, and energy levels of hydrogen and hydrogen-like atoms.
Nuclear fission, fusion, and energy production
Understand the processes of nuclear fission and fusion, their energy yields, the role of binding energy, and applications like nuclear reactors and solar energy.
Mass defect, binding energy, and mass-energy equivalence
Learn how mass defect leads to nuclear binding energy, the use of E=mc², and how to calculate binding energy per nucleon and related quantities.
Nuclear size, radius, and density
Explore how nuclear size is measured, the formula for nuclear radius, its dependence on mass number, and the concept of nuclear density.
Nuclear reactions and conservation laws
Study the equations for nuclear reactions, including conservation of mass number, atomic number, and other physical quantities.