Kinetic, Potential, and Total Energy
For a circular orbit in a 1/r attractive potential, the virial relation gives U = -2K and E = K + U = -K = U/2. As an electron falls to lower n, K rises while U and E decrease.
Why this shows up in the exam
Comparing energy components · Tracking signs during de-excitation · Checking Bohr-orbit calculations
Learn the idea
In a Coulomb Bohr orbit, kinetic energy is positive, potential energy is twice as negative, and total energy is negative. The electron moves, so it has positive kinetic energy, but attraction gives a larger negative potential energy. Their sum leaves the atom bound.
🧠 Memory hook: K is plus one share, U is minus two, total is minus one.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- U = -2K — Coulomb-orbit virial relation
- E = -K = U/2 — total energy in a circular Coulomb orbit
- K_n = 13.6 Z²/n² eV — kinetic energy magnitude for a hydrogen-like level
How to approach it
- 1Write U = -2K before substituting values
- 2Form E = K + U
- 3For a transition, compare the 1/n² magnitudes and signs
Common slip-ups that cost marks
- •Claiming all three energies decrease in a downward transition
- •Using U = -K
- •Applying the Coulomb ratio to an arbitrary potential
🌟 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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