The radius of the first permitted Bohr orbit for the electron, in a hydrogen atom equals and its ground state energy equals . If the electron in the hydrogen atom is replaced by muon [charge same as electron and mass ], the first Bohr radius and groun

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Q.
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 in the hydrogen atom is replaced by muon $(μ^{-})$ [charge same as electron and mass $207 m_{e}$ ], the first Bohr radius and ground state energy will be [2019]

1 $0.53 \times 10^{- 13} m, - 3.6 eV$

2 $25.6 \times 10^{- 13} m, - 2.8 eV$

3 $2.56 \times 10^{- 13} m, - 2.8 keV$

4 $2.56 \times 10^{- 13} m, - 13.6 eV$

Ans.
(3)

Given, radius of first Bohr orbit for electron in a hydrogen atom, $r = 0.51$ $Å$

and its ground state energy, $E_{n} = - 13.6$ $eV$

Charge of muon = charge of electron

Mass of muon = 207 $\times$ (mass of electron)

Therefore, when electron is replaced by muon, then first Bohr radius, $r'_{1} = \frac{0.51 Å}{207} = 2.56 \times 10^{- 13} m$ and ground state energy,

$E'_{1} = - 13.6 \times 207 = - 2815.2$ $eV = - 2.815$ $keV$

Solution

1 $0.53 \times 10^{- 13} m, - 3.6 eV$

2 $25.6 \times 10^{- 13} m, - 2.8 eV$

3 $2.56 \times 10^{- 13} m, - 2.8 keV$

4 $2.56 \times 10^{- 13} m, - 13.6 eV$

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Solution

1 0.53×10-13m,-3.6eV

2 25.6×10-13m,-2.8eV

3 2.56×10-13m,-2.8keV

4 2.56×10-13m,-13.6eV

Want Us to Email you About Special Offers & Updates?

1 $0.53 \times 10^{- 13} m, - 3.6 eV$

2 $25.6 \times 10^{- 13} m, - 2.8 eV$

3 $2.56 \times 10^{- 13} m, - 2.8 keV$

4 $2.56 \times 10^{- 13} m, - 13.6 eV$