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
The frequency of in the first Bohr orbit in a H-atom is:
The frequency of \( e^{-} \) in the first Bohr orbit in a H-atom is:
- A. \( 6530 \times 10^{12} \mathrm{Hz} \)
- B. \( 6840 \times 10^{12} \mathrm{Hz} \)
- C. \( 6430 \times 10^{12} \mathrm{Hz} \)
- D. \( 6734 \times 10^{12} \mathrm{Hz} \)
Step-by-step solution
The frequency of an electron in the first Bohr orbit of hydrogen is derived from f = (m e^4) / (4 ε0^2 h^3). Using approximate constants (m=9.1×10⁻³¹ kg, e=1.6×10⁻¹⁹ C, ε0=8.85×10⁻¹² F/m, h=6.63×10⁻³⁴ J s), the calculation yields f ≈ 6.53×10¹⁵ Hz = 6530×10¹² Hz, matching option A.
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