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Chemistry · Bohr model of a hydrogen atom: its postulates, derivation of the relations for the energy of the electron and radii of the different orbits, limitations of Bohr's model

From Bohr's model, radius of the orbit and energy of the hydrogen atom are calcu

From Bohr's model, radius of the orbit and energy of the hydrogen atom are calculated as: This question has multiple correct options

  • A. the radius of the \( 1^{s t} \) orbit is \( 0.529 A^{\circ} \)
  • B. the energy of the \( 1^{s t} \) orbit is \( -13.6 e V \)
  • C. the energy of the \( 1^{s t} \) orbit is \( -21.72 \times 10^{-19} J \)
  • D. the radius of the \( 1^{s t} \) orbit is \( 1.06 A^{\circ} \)

Step-by-step solution

According to Bohr's model, the radius of the first orbit (n=1) of a hydrogen atom is given by r₁ = a₀ = 0.529 Å (the Bohr radius). This value is derived from the quantization of angular momentum and the electrostatic force balance. The other options: B is also correct (energy -13.6 eV), C is approximately correct but not exact (-13.6 eV = -2.18×10⁻¹⁸ J = -21.8×10⁻¹⁹ J, not -21.72×10⁻¹⁹ J), and D is incorrect (radius 1.06 Å corresponds to n=2). Since the question asks for the single best correct option, A is the most precise and accurate.
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