If muonic hydrogen atom is an atom in which a negatively charged muon (μ) of mass about 207 me revolves around a proton, then first Bohr radius of this atom is (re = 0.53 × 10-10 m)

Question

If muonic hydrogen atom is an atom in which a negatively charged muon (μ) of mass about 207 me revolves around a proton, then first Bohr radius of this atom is (re = 0.53 × 10-10 m) (A) 2.56 × 10-10 m (B) 2.56 × 10-11 m (C) 2.56 × 10-12 m (D) 2.56 × 10-13 m

Tardigrade Admin · Accepted Answer

According to Bohrâs atomic model, r propto (1/m) ⇒ (rμ/re) = (me/mμ) ...(i) Here, re = 0.53 ×10-10 m ; mμ = 207 me ∴ rμ = (me/207 me) ×0.53 ×10-10 (using (i)) = 2.56×10-13m

Q. If muonic hydrogen atom is an atom in which a negatively charged muon ( $μ$ ) of mass about $207 m_{e}$ revolves around a proton, then first Bohr radius of this atom is $(r_{e} = 0.53 \times 1 0^{- 10} m)$

$2.56 \times 1 0^{- 10} m$

$2.56 \times 1 0^{- 11} m$

$2.56 \times 1 0^{- 12} m$

$2.56 \times 1 0^{- 13} m$

Q. If muonic hydrogen atom is an atom in which a negatively charged muon (μ) of mass about 207me​ revolves around a proton, then first Bohr radius of this atom is (re​=0.53×10−10m)

2.56×10−10m

2.56×10−11m

2.56×10−12m

2.56×10−13m

According to Bohr’s atomic model, r∝m1​ ⇒re​rμ​​=mμ​me​​...(i) Here, re​=0.53×10−10m; mμ​=207me​ ∴rμ​=207me​me​​×0.53×10−10 (using (i)) =2.56×10−13m

Q. If muonic hydrogen atom is an atom in which a negatively charged muon ( $μ$ ) of mass about $207 m_{e}$ revolves around a proton, then first Bohr radius of this atom is $(r_{e} = 0.53 \times 1 0^{- 10} m)$

$2.56 \times 1 0^{- 10} m$

$2.56 \times 1 0^{- 11} m$

$2.56 \times 1 0^{- 12} m$

$2.56 \times 1 0^{- 13} m$