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A formula analogous to Rydberg formula a...

A formula analogous to Rydberg formula applies to the series of spectral ines which arise from transition 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,t he '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:
`(1)/(lamda)=R_(H)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))](R_(H)=109678cm^(-1))`
Q. Angular momentum of 'muon' in muonic hydrogen atom may be given as:

A

`(h)/(pi)`

B

`(h)/(2pi)`

C

`(h)/(4pi)`

D

`(h)/(6pi)`

Text Solution

Verified by Experts

The correct Answer is:
B
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Energy Level Of Hydrogen Atoms

Hydrogen Atom and Hydrogen Molecule The observed wavelengths in the line spectrum of hydrogen atom were first expressed in terms of a series by johann Jakob Balmer, a Swiss teacher. Balmer's empirical empirical formula is 1/lambda=R_(H)(1/2^(2)-1/n^(2))," " N=3, 4, 5 R_(H)=(Me e^(4))/(8 epsilon_(0)^(2)h^(3) c)=109. 678 cm^(-1) Here, R_(H) is the Rydberg Constant, m_(e) is the mass of electron. Niels Bohr derived this expression theoretically in 1913. The formula is easily generalized to any one electron atom//ion. A formula analogous to Balmer's formula applies to the series of spectral lines which arise from transition from higher energy levels to the lowest energy level of hydrogen atom. Write this formula and use it to determine the ground state energy of a hydrogen atom in eV. A 'muonic hydrogen atom' is like a hydrogen atom in which the electron is replaced by a heavier particle, the muon. The mass of a muon is about 207 times the mass of an electron, while its charge is the same as that of an electron. A muon has a very short lifetime, but we ignore its ubstable nature here.

Knowledge Check

  • A formula analogous to Rydberg formula applies to the series of spectral ines which arise from transition 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,t he '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: (1)/(lamda)=R_(H)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))](R_(H)=109678cm^(-1)) Q. Energy of first Bohr orbit of muonic hydrogen atom is:

    A
    `-(13.6)/(207)eV`
    B
    `13.6xx207eV`
    C
    `+(13.6)/(207)eV`
    D
    `+13.6xx207eV`

  • A formula analogous to Rydberg formula applies to the series of spectral ines which arise from transition 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,t he '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: (1)/(lamda)=R_(H)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))](R_(H)=109678cm^(-1)) Q. Radius of first Bohr orbit of muonic hydrogen atom is:

    A
    `(0.259)/(207)`Ã…
    B
    `(0.529)/(207)`Ã…
    C
    `0.529xx207`Ã…
    D
    `0.259xx207`Ã…

  • A formula analogous to Rydberg formula applies to the series of spectral ines which arise from transition 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,t he '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: (1)/(lamda)=R_(H)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))](R_(H)=109678cm^(-1)) Q. Distance between first and third Bohr orbits of muonic hydrogen atom will be:

    A
    `(0.529)/(207)xx2`Ã…
    B
    `(0.529)/(207)xx7`Ã…
    C
    `(0.529)/(207)xx8`Ã…
    D
    `(0.529)/(207)`Ã…

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