The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals 0.51 Å and its ground state energy equals -13.6 eV. If the electron is replaced by a muon with the same charge and mass 207mₑ, the first Bohr radius and ground-state energy will be:
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Question

The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals 0.51 Å and its ground state energy equals -13.6 eV. If the electron is replaced by a muon with the same charge and mass 207mₑ, the first Bohr radius and ground-state energy will be:

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G1 Physics · Accepted Answer

Bohr radius r ∝ 1/m. Therefore r′ = 0.51 × 10⁻¹⁰/207 ≈ 2.46 × 10⁻¹³ m (approximately 2.56 × 10⁻¹³ m if 0.53 Å is used). Bohr energy E ∝ m, so E′ = −13.6 × 207 eV ≈ −2.8 keV. Answer: C.

The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals 0.51 Å and its ground state energy equals −13.6 eV. If the electron is replaced by a muon with the same charge and mass 207mₑ, the first Bohr radius and ground-state energy will be: