NEET 2019 Odisha · PhysicsOrbit radiusPrevious Year Question
The radius of the first permitted Bohr orbit for the electron in a hydrogen atom is 0.51 Å and its ground state energy is –13.6 eV. If the electron in hydrogen is replaced by a muon (μ⁻) [charge same as electron, mass 207 mₑ], the first Bohr radius and ground state energy will be:
Answer: (C) 2.56 × 10⁻¹³ m, –2.8 keV. Answer: (c) 2.56 × 10⁻¹³ m, –2.8 keV Solution: Bohr radius r ∝ 1/m and energy E ∝ m (at fixed Z).
- A.0.53 × 10⁻¹³ m, –3.6 eV
- B.25.6 × 10⁻¹³ m, –2.8 eV
- C.2.56 × 10⁻¹³ m, –2.8 keV✓
- D.2.56 × 10⁻¹³ m, –13.6 eV
Correct Answer
(C) 2.56 × 10⁻¹³ m, –2.8 keV
Solution & Explanation
Answer: (c) 2.56 × 10⁻¹³ m, –2.8 keV Solution: Bohr radius r ∝ 1/m and energy E ∝ m (at fixed Z). Replacing the electron by a muon of mass 207mₑ: r_μ = r_e/207 = 0.51 Å/207 = 0.51×10⁻¹⁰/207 = 2.46×10⁻¹³ m ≈ 2.56×10⁻¹³ m. E_μ = 207 × (−13.6 eV) = −2815 eV ≈ −2.8 keV.
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