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A monochromatic light beam with energy 204eV is used to excite the Be+3 (H –like atom with Z=4) from its ground state to some excited state m. Neglect the finite nuclear mass correction.

a) Find the quantum number m of this excited state.
b) Following this transition the excited Be+3 atom emits a spectral line at 30.42nm as a result of the transition from this excited state m to some other lower state n. Find the quantum number of this new state.
c) Calculate the orbital radius of the electron in the state n.

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  1. (a) For BeIII with Z=4, use the Rydberg equation for the energy levels. They will be 4^2 = 16 times more widely separated than for hydrogen.

    E(m) = 13.58 eV*16/n^2 = 217.3 /m^2 eV

    For a transition from the ground state (m=1),

    204 eV = 217.3/1 - 217.3/m^2
    217.3/m^2 = 16.4

    m = 4 (probably) There may be some accuracy issues with the value of the Rydberg that I used.

    (b) Convert the wavelength to photon energy in eV. Then use the Rydberg equation to compute n.

    E = h*c/(wavelength) = ____ eV

    E = 204 eV - R/n^2 = 204 - 217.3/n^2
    Solve for n

    (c) Bohr orbit radius = ao * n^2/Z
    where ao is the hydrogen ground state Bohr radius

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