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Bohr Model Energy Levels and Hydrogen Spectrum

A hydrogen atom in the ground state is bombarded with a 12.5 eV electron beam. What is the maximum energy level the elec

**Excitation** energy required to go from n=1 to n=3 is 12.09 eV, from ground to n=∞ ionization 13.6 eV, state n=∞ means ionized, electron free with zero energy, highest level reached by electron beam energy determines which levels can be excited, e.g., 11 eV beam from ground can reach n=2 (10.2 eV) but not n=3 (12.09 eV), so max n=2. E₁ = -13.6 eV . E_n = -13.6 + 12.5 = -1.1 eV . -1.1 = -(13.6/n²) ⇒ n² ≈ 12.36 ⇒ n = 3 (since E₃ = -1.51 eV < -1.1 eV , n = 3 ). Using E_n = -13.6/n² eV, r_n =

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

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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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Bohr Model Energy Levels and Hydrogen Spectrum

An electron beam of 11.0 eV excites a hydrogen atom in the ground state. What is the highest energy level reached? (Use

**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 + 11.0 = -2.6 eV . -2.6 = -(13.6/n²) ⇒ n² ≈ 5.23 ⇒ n = 2 (since E₂ = -3.4 eV < -2.6 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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