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A Lyman transition in the Bohr hydrogen atom: which expressions give the change in kinetic energy, de Broglie wavelength, total energy and the photon frequency

A Bohr hydrogen atom whose electron, drawn with its de Broglie standing wave, jumps from orbit n to orbit 1 and emits an ultraviolet Lyman photon. The run measures v, r, K and lambda before and after and checks each option's expression against the measured change: (A) |dK| and (C) nu hold, (B) misses the 1/n and (D) is twice |dE|.

Sub-topics covered

• Bohr quantisation m v r = k h/2pi and the Coulomb force: v ~ 1/k, r ~ k^2, K ~ 1/k^2
• Kinetic energy K_k = (h/4pi) k v_k/r_k = e^2/(8 pi eps0 r_k); total energy E_k = -K_k
• de Broglie wavelength lambda_k = 2 pi r_k/k = e^2/(4 eps0 k K_k): k wavelengths on orbit k
• Lyman series: h nu = E_n - E_1 = e^2/(8 pi eps0)(1/r_1 - 1/r_n), ultraviolet

What it teaches

• From m v r = k hbar, K_k = (1/2)(m v_k r_k)(v_k/r_k) = (h/4pi) k v_k/r_k, so |dK| = (h/4pi)|n v_n/r_n - v_1/r_1| - statement (A)
• E = -K, so |dE| = |dK|; statement (D) has h/2pi and is twice the change
• The photon carries h nu = K_1 - K_n = e^2/(8 pi eps0)(1/r_1 - 1/r_n) - statement (C)
• lambda_k = e^2/(4 eps0 k K_k), so statement (B) misses the 1/n and is (n + 1) times the true change

Simulation ID

• ADV-2026-P1-PHY-Q05 · revision 1

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