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#hydrogen ionization

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Bohr Model Energy Levels and Hydrogen Spectrum

What is the energy required to ionize a hydrogen atom from its ground state? (Ground state energy = -13.6 eV)

**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. Ionization energy = energy to reach E = 0 from ground state. E₁ = -13.6 eV , E_∞ = 0 eV . Energy required = 0 - (-13.6) = 13.6 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 1 u

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

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Atomic Models - Rutherford, Thomson and Bohr

Which of the following statements is correct about the ionization energy of a hydrogen atom in Bohr’s model?

**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. The ionization energy is the energy required to remove the electron from the ground state ( n = 1 , -13.6 eV) to infinity (0 eV), which is 13.6 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 1 u

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

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Atomic Models - Rutherford, Thomson and Bohr

In Bohr’s model, what is the state of a hydrogen atom when its electron is in the \( n = \infty \) orbit?

**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. At n = ∞ , the energy is zero, meaning the electron is ionized and no longer bound to the nucleus. 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 MeV, evaluation yields Ionized state, consistent with

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

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