An electron beam of 12.0 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 + 12.0 = -1.6 eV . -1.6 = -(13.6/n²) ⇒ n² ≈ 8.5 ⇒ n = 2 (since E₂ = -3.4 eV < -1.6 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