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(D) The ionization energy of a hydrogen-like species is given by $E_n = -13.6 	imes Z^2 / n^2 \, eV$ or $E_n = -E_H 	imes Z^2 / n^2$.For $Li$ $(Z=3)

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$1$

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(D) The ionization energy of a hydrogen-like species is given by $E_n = -13.6 	imes Z^2 / n^2 \, eV$ or $E_n = -E_H 	imes Z^2 / n^2$.For $Li$ $(Z=3)$ in the ground state $(n=1)$,the energy required to remove the electron is $E = E_{\infty} - E_1 = 0 - (-2.2 	imes 10^{-18} 	imes 3^2 / 1^2) = 19.8 	imes 10^{-18} \, J$.The energy of a photon is $E = hc / \lambda$,so $\lambda = hc / E$.Substituting the values: $\lambda = (6.63 	imes 10^{-34} 	imes 3 	imes 10^8) / (19.8 	imes 10^{-18}) = 19.89 	imes 10^{-26} / 19.8 	imes 10^{-18} \approx 1.0045 	imes 10^{-8} \, m$.Comparing this with $x 	imes 10^{-8} \, m$,we get $x \approx 1$.

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