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#excitation energy

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Bohr Model Energy Levels and Hydrogen Spectrum

What is the energy required to excite a hydrogen atom from \( n = 1 \) to \( n = 3 \)? (Use \( E_n = -\frac{13.6}{n^2} \

**Bohr energy levels** E_n = -13.6/n² eV for hydrogen, negative indicating bound state, total energy = -13.6 eV ground state n=1, -3.4 eV n=2, -1.51 eV n=3, etc., photon energy for transition n_i → n_f is ΔE =13.6(1/n_f² -1/n_i²) eV, wavelength λ = hc/ΔE, h=6.6×10⁻³⁴ J·s, c=3×10⁸ m/s. Emission line spectrum characterized by discrete wavelengths because energy levels discrete. E₁ = -13.6 eV , E₃ = -1.51 eV . Δ E = -1.51 - (-13.6) = 12.09 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 u = 931.5

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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