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#hydrogen excitation

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De Broglie Hypothesis and Quantization in Bohr Model

What is the minimum energy required to excite a hydrogen atom from its ground state to the first excited state? (Use \(

**De Broglie hypothesis** λ = h/p, p=mv momentum, suggests electron as wave, in Bohr model circumference 2πr = n λ, standing wave condition, n wavelengths fit into orbit, for n=6, 6 wavelengths, for n=4, 4 wavelengths, explains quantization of angular momentum L = r p = r h/λ = r h n/(2πr)= n h/2π = n ħ, physical basis for Bohr quantization. E₁ = -13.6 eV , E₂ = -3.4 eV . Δ E = -3.4 - (-13.6) = 10.2 eV . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1

Ref: NCERT > Physics Book > Atoms and Nuclei > De Broglie Hypothesis and Quantization in Bohr Model

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Atomic Models - Rutherford, Thomson and Bohr

A photon of energy 10.2 eV is absorbed by a hydrogen atom in the ground state. To which energy level does the electron j

**Bohr's stationary orbits** defined by angular momentum quantization L = n ħ, ħ = h/2π, n=1 ground state, electron in these orbits does not radiate despite acceleration, contrary to classical EM theory which predicts atom collapse due to energy loss via radiation, Bohr postulates to explain observed stability and discrete spectra. E₁ = -13.6 eV . E_n = E₁ + 10.2 = -13.6 + 10.2 = -3.4 eV . -3.4 = -(13.6/n²) ⇒ n² = 4 ⇒ n = 2 . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1 u

Ref: NCERT > Physics Book > Atoms and Nuclei > Atomic Models - Rutherford, Thomson and Bohr

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Bohr Model Energy Levels and Hydrogen Spectrum

A 13.0 eV electron beam excites a hydrogen atom in the ground state. What is the highest energy level reached? (Use \( E

**Hydrogen transitions** example n=3→n=1 ΔE=13.6(1-1/9)=12.09 eV, photon 12.09 eV, λ=1240/12.09≈102.6 nm Lyman series, n=3→n=2 ΔE=1.89 eV Balmer visible Hα 656 nm. Absorption photon energy must match difference, if atom in n=2 absorbs 1.89 eV jumps to n=3, if absorbs 12.75 eV from ground 1→4 because -13.6+12.75=-0.85 eV = -13.6/16. E₁ = -13.6 eV . E_n = -13.6 + 13.0 = -0.6 eV . -0.6 = -(13.6/n²) ⇒ n² ≈ 22.67 ⇒ n = 4 (since E₄ = -0.85 eV < -0.6 eV ). Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and

Ref: NCERT > Physics Book > Atoms and Nuclei > Bohr Model Energy Levels and Hydrogen Spectrum

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