What is the energy required to excite a hydrogen atom from n=1 to n=3?

E₁ = −13.6 eV; E₃ = −13.6/9 = −1.51 eV. Energy required = E₃ − E₁ = −1.51 − (−13.6) = 12.09 eV. A photon of energy 12.09 eV (λ ≈ 103 nm, UV) is absorbed.

Why are only certain wavelengths seen in hydrogen spectrum?

Electrons in hydrogen can only exist in certain quantized energy levels (n=1,2,3…). When an electron transitions between two specific levels, it emits a photon of exactly E = hν = E_high − E_low. Since the energy levels are discrete, only specific photon energies (wavelengths) are emitted, producing a line spectrum rather than a continuous spectrum.

Why is the Balmer series visible while Lyman series is ultraviolet?

The Lyman series involves transitions to n=1 (ground state), releasing high energy photons (E > 10 eV) corresponding to UV wavelengths (<400 nm). The Balmer series involves transitions to n=2, releasing lower energy photons (1.9–3.4 eV) with wavelengths in the visible range (400–700 nm). Human eyes can detect the Balmer series wavelengths.

Bohr's Model of the Atom and Hydrogen Spectrum

Atoms and Nuclei • Class 12 Physics • NCERT • CBSE

Bohr radius: a₀ = 0.529 Å. Energy of nth orbit: Eₙ = −13.6/n² eV. Wave number: 1/λ = RH(1/n₁² − 1/n₂²). Rydberg constant RH = 1.097 × 10⁷ m⁻¹.

Key Formulas

Bohr radius: rₙ = n² × 0.529 Å
Energy: Eₙ = −13.6/n² eV
Rydberg: 1/λ = RH(1/n₁² − 1/n₂²)
RH = 1.097 × 10⁷ m⁻¹
Angular momentum: mvr = nħ
Ionisation energy of H = 13.6 eV

Frequently Asked Questions

What is the energy required to excite a hydrogen atom from n=1 to n=3?: E₁ = −13.6 eV; E₃ = −13.6/9 = −1.51 eV. Energy required = E₃ − E₁ = −1.51 − (−13.6) = 12.09 eV. A photon of energy 12.09 eV (λ ≈ 103 nm, UV) is absorbed.
Why are only certain wavelengths seen in hydrogen spectrum?: Electrons in hydrogen can only exist in certain quantized energy levels (n=1,2,3…). When an electron transitions between two specific levels, it emits a photon of exactly E = hν = E_high − E_low. Since the energy levels are discrete, only specific photon energies (wavelengths) are emitted, producing a line spectrum rather than a continuous spectrum.
Why is the Balmer series visible while Lyman series is ultraviolet?: The Lyman series involves transitions to n=1 (ground state), releasing high energy photons (E > 10 eV) corresponding to UV wavelengths (<400 nm). The Balmer series involves transitions to n=2, releasing lower energy photons (1.9–3.4 eV) with wavelengths in the visible range (400–700 nm). Human eyes can detect the Balmer series wavelengths.

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