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  4. The ionisation potential of hydrogen atom is -13.6 eV. An electron in the ground state of a hydrogen atoms absorbs a photon of energy 12.75 eV. How many different spectral line can one expect when the electron make a downward transition?

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Q. The ionisation potential of hydrogen atom is $-13.6\,eV$. An electron in the ground state of a hydrogen atoms absorbs a photon of energy $12.75 \,eV$. How many different spectral line can one expect when the electron make a downward transition?

WBJEEWBJEE 2008Atoms

Solution:

$E=E_{1} / n^{2}$
Energy used for excitation is $12.75\, eV$
$i e,(-13.6+12.75) eV =-0.85\, eV$
image
Energy levels of H-atom
The photons of energy $12.75\, eV$ can excite the
fourth level of $H$-atom. Therefore, six lines will be emitted, $\left(n \frac{(n-1)}{2}\right.$ lines $)$