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The observed wavelegnth in the line spec...

The observed wavelegnth in the line spectrum of hydrogen atom were first expressed in terms of a series by Johann Jakob Balmer, a Swiss teacher.
Balmer's emipirical formula is
`(1)/(lamda)=R_(H)[(1)/(2^(2))-(1)/(n^(2))]n=3,4,5` . . .
`R_(H)=109678cm^(-1)` is the Rydberg constant.
Niels Bohr derived this expression theoretically in 1913. The formula is generalised to any one electron atom/ion.
Q. Calculat ethe longest wavelength in Ã…(1Ã…=`10^(-10)m`) in the balmer series of singly ionized helium `He^(+)`. Select the correct answer. Ignore the nuclear motion in your calculation.

A

2651Ã…

B

1641.1Ã…

C

6569Ã…

D

3249Ã…

Text Solution

Verified by Experts

The correct Answer is:
B
`(1)/(lamda_(He^(+)))=R_(H)Z^(2)[(1)/(2^(2))-(1)/(3^(2))]`
`=109678xx4[(5)/(36)]`
`lamda_(He^(+))=1641.1`Ã…
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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. Calculate the iongest wavelength in A (1 Å=10^(-10) m) in the 'Balmer series of singly ionized helium (He^(+)) Ignore nuclear motion in your calculation.

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. H^(-) is a two-electron atomic system. Assuming that the Bohr energy formula is valid for each electron with nuclear charge Z replaced by Z_(eff') calculate Z_(eff) for H^(-) .

Knowledge Check

  • The observed wavelegnth in the line spectrum of hydrogen atom were first expressed in terms of a series by Johann Jakob Balmer, a Swiss teacher. Balmer's emipirical formula is (1)/(lamda)=R_(H)[(1)/(2^(2))-(1)/(n^(2))]n=3,4,5 . . . R_(H)=109678cm^(-1) is the Rydberg constant. Niels Bohr derived this expression theoretically in 1913. The formula is generalised to any one electron atom/ion. Which of the following is not correctly matched?

    A
    `H_(alpha)-`6569Ã…(Red)
    B
    `H_(beta)-`4861Ã…
    C
    `H_(gamma)-`4340Ã… (Orange)
    D
    `H_(delta)-`4101Ã…(Violet)

  • The observed wavelegnth in the line spectrum of hydrogen atom were first expressed in terms of a series by Johann Jakob Balmer, a Swiss teacher. Balmer's emipirical formula is (1)/(lamda)=R_(H)[(1)/(2^(2))-(1)/(n^(2))]n=3,4,5 . . . R_(H)=109678cm^(-1) is the Rydberg constant. Niels Bohr derived this expression theoretically in 1913. The formula is generalised to any one electron atom/ion. The wavelength of first line of Balmer spectrum of hydrogen will be:

    A
    4340Ã…
    B
    4101Ã…
    C
    6569Ã…
    D
    4861Ã…

  • The observed wavelegnth in the line spectrum of hydrogen atom were first expressed in terms of a series by Johann Jakob Balmer, a Swiss teacher. Balmer's emipirical formula is (1)/(lamda)=R_(H)[(1)/(2^(2))-(1)/(n^(2))]n=3,4,5 . . . R_(H)=109678cm^(-1) is the Rydberg constant. Niels Bohr derived this expression theoretically in 1913. The formula is generalised to any one electron atom/ion. Q.In which region of electromagnetic spectrum does the Balmer series lie?

    A
    UV
    B
    Visible
    C
    Infrared
    D
    Far infrared

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