Angular-Momentum Quantization
Bohr's quantization condition restricts orbital angular momentum magnitude to positive integer multiples of hbar. It is equivalent to fitting an integer number of de Broglie wavelengths around the circular orbit.
Why this shows up in the exam
Finding an orbit number from angular momentum · Calculating angular-momentum change during excitation · Connecting Bohr quantization with matter waves
Learn the idea
The nth Bohr orbit carries angular momentum n hbar. Each allowed orbit adds one quantum of angular momentum. Moving from n_i to n_f changes orbital angular momentum by the difference in their integer labels times hbar.
🧠 Memory hook: Orbit number counts hbar packets.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- m v_n r_n = n hbar — quantized orbital angular momentum
- Delta L = (n_f - n_i) hbar — change in Bohr orbital angular momentum
How to approach it
- 1Rewrite every hbar as h/(2 pi) if needed
- 2Solve for the integer n
- 3Use final minus initial when a change is requested
Common slip-ups that cost marks
- •Using n h instead of n hbar
- •Allowing n = 0 for a Bohr orbit
- •Using photon spin to calculate the Bohr orbital value
🌟 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.
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