An electron from the nth excited state of hydrogen emits a photon while returning to the ground state. Let λₙ be the electron de Broglie wavelength in the nth orbit and Λₙ the emitted-photon wavelength. For large n, which relation is correct?
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Question

An electron from the nth excited state of hydrogen emits a photon while returning to the ground state. Let λₙ be the electron de Broglie wavelength in the nth orbit and Λₙ the emitted-photon wavelength. For large n, which relation is correct?

Options

G1 Physics · Accepted Answer

Step 1: Use λ = h/p and, for non-relativistic motion, p = √(2mK). Step 2: For particles accelerated through a potential V, λ = h/√(2mqV). Step 3: Apply momentum/energy conservation if a collision is involved. Final: D: Λₙ ≈ A + B/λₙ².