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    Wavelength of the transition

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    A hydrogen-like ion has a nucleus of charge +Ze and a single electron outside this nucleus. The energy levels of these ions are -ZsquaredRH/n2 (where Z = atomic number). Calculate the wavelength of the transition from n=3 to n=2 for He+, a hydrogen-like ion. In what region of the spectrum does this emission occur?

    © BrainMass Inc. brainmass.com December 24, 2021, 4:56 pm ad1c9bdddf
    https://brainmass.com/physics/bohr-theory/wavelength-transition-17638

    SOLUTION This solution is FREE courtesy of BrainMass!

    E= h c R (Z ^2) / (n^2)

    h= Planck's constant= 6.6261x 10 ^(- 34) J s
    c=speed of light=3 x 10 ^ 8 m/s
    R=Rydberg constant= 1.09678 x 10 ^ 7 (m^ -1)

    hcR= 2.18021E-18 Joules
    This can also be expressed in electron volts (eV)
    1 e V=1.602 x 10 ^ -19 Joules

    Thus we divide the energy in Joules by 1.602 x 10 ^ -19 to get the energy in eV
    or
    hcR= 13.61 eV

    Or E=13.61 (Z^2)/(n^2)

    For Helium Z= 2
    Thus E=13.61*2^2 / n^2 = 54.44 / n^2 eV

    delta E=54.44 *{ 1/(n1 ^2)- 1/(n2 ^2)} eV
    For transition from n=3 to n=2
    n1= 2
    n2= 3

    or delta E= 7.56 eV

    delta E=h nu =h c / lambda = 7.56 eV= 1.2111E-18 Joules

    where E-18 denotes 10^-18

    or lambda =hc/delta E= 1.64134E-07 m
    which is equal to 1641.34 Angstrom or 164.134 nm

    This is in the ultraviolet region of the spectrum

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:56 pm ad1c9bdddf>
    https://brainmass.com/physics/bohr-theory/wavelength-transition-17638

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