A formula analogous to the Rydberg formula applies to the series of spectral lines which arise from transitions from higher energy level to the lower energy level of hydrogen atom.
A muonic hydrogen atom is like a hydrogen atom in which the electron is replaced by a heavier particle, the 'muon'. The mass of the muon is about $207$ times the mass of an electron, while the charge remains same as that of the electron. Rydberg formula for hydrogen atom is:
$\frac{1}{λ} = R_{H} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] (R_{H} = 109678 {c m}^{- 1})$
Distance between first and third Bohr orbits of muonic hydrogen atom will be

\frac{0.529}{207} \times 2 ˚ A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{0.529}{207} \times 7 ˚ A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{0.529}{207} \times 8 ˚ A

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{0.529}{207} ˚ A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{0.529}{207} \times 8 ˚ A$
$r_{1} = \frac{0.529 A^{o}}{207}$
$r_{3} = \frac{0.529 A^{o}}{207} \times n^{2}$
$r_{3} = \frac{0.529 A^{o}}{207} \times 3^{2}$
$r_{3} = \frac{0.529 A^{o}}{207} \times 9$
$r_{3} - r_{1} = \frac{0.529 A^{o}}{207} \times 9 - \frac{0.529 A^{o}}{207}$
$r_{3} - r_{1} = \frac{0.529 A^{o}}{207} \times 8$
Distance between first and third Bohr orbits of muonic hydrogen atom will be $r_{3} - r_{1} = \frac{0.529 A^{o}}{207} \times 8$

Suggest Corrections

Similar questions

A formula analogous to the Rydberg formula applies to the series of spectral lines which arise from transitions from higher energy level to the lower energy level of hydrogen atom.
A muonic hydrogen atom is like a hydrogen atom in which the electron is replaced by a heavier particle, the 'muon'. The mass of the muon is about

207

times the mass of an electron, while the charge remains same as that of the electron. Rydberg formula for hydrogen atom is:

\frac{1}{λ} = R_{H} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] (R_{H} = 109678 {c m}^{- 1})

Angular momentum of 'muon' in muonic hydrogen atom may be given as:

Q. Imagine that the electron in a hydrogen atom is replaced by a muon (

μ

). The mass of muon particle is

207

times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be:

Obtain the first Bohr’s radius and the ground state energy of a muonic hydrogen atom [i.e., an atom in which a negatively charged muon (μ⁻) of mass about 207m_e orbits around a proton].

Q. A

μ - m e s o n

(charge

- e

, mass

= 207 m

, where

m

is the mass of the electron) can be captured by a proton to form a hydrogen-like "mesic" atom. Calculate the radius of the first Bohr orbit, the binding energy, and the wavelength of the line in the Lyman series for such an atom. The mass of the proton is

1836

times the mass of the electron. The radius of the first Bohr orbit and the binding energy of Hydrogen are

0.529 ˚ A

and

13.6 e V

, respectively. Take

R = 109678 c m^{- 1}

Q. Calculate the wavelength of the spectral line, when an electron in the hydrogen atom undergoes a transition from the energy level 4 to energy level 2.

R_{H} = 109678 c m^{- 1}

Join BYJU'S Learning Program

The correct option is C 0.529207×8˚Ar1=0.529Ao207r3=0.529Ao207×n2 r3=0.529Ao207×32 r3=0.529Ao207×9 r3−r1=0.529Ao207×9−0.529Ao207r3−r1=0.529Ao207×8 Distance between first and third Bohr orbits of muonic hydrogen atom will be r3−r1=0.529Ao207×8