If the radius of the first orbit of the hydrogen atom is 0.53 A ∘ , then the de-Broglie wavelength of the electron in the ground state of hydrogen atom will be

Question

If the radius of the first orbit of the hydrogen atom is 0.53 A ∘ , then the de-Broglie wavelength of the electron in the ground state of hydrogen atom will be, 0.53 A ∘, 3.33 A ∘, 1.67 A ∘, 1.06 A ∘

MARKS App · Accepted Answer

According to Bohr's quantization condition m v r = n h 2 π ∴ h m v = 2 π r n ... (i) ∵ de-Broglie wavelength λ = h m v ... (ii) From Eqs. (i) and (ii), λ = 2 π r n ∵ Electron in the ground state r = 0.53 A ∘ and n = 1 ⇒ λ = 2 π × 0.53 A ∘ 1 = 3.33 A ∘

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