Find the de Broglie wavelength of the electron in the n = 2 orbit of hydrogen. Take the Bohr radius a₀ = 0.052 nm.
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Question

Find the de Broglie wavelength of the electron in the n = 2 orbit of hydrogen. Take the Bohr radius a₀ = 0.052 nm.

G1 Physics · Accepted Answer

Step 1: For hydrogen, the Bohr orbit radius is rₙ = n²a₀ (Z = 1). Step 2: At n = 2, r₂ = 4 × 0.052 = 0.208 nm. Step 3: Standing-wave condition is 2πrₙ = nλ. Step 4: Therefore λ = 2πr₂/2 = π × 0.208 nm ≈ 0.653 nm. Step 5: The closest printed choice is 0.67 nm. Final answer: Approximately 0.67 nm, Option B.