Which of the following energy changes is less | vedclass

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(B) The energy of the third Balmer transition in $He^{\oplus}$ $(Z=2)$ corresponds to the transition from $n=5$ to $n=2$.$\Delta E = 13.6 	imes Z^{2}

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Third separation energy of $Li^{2+}$ ion

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(B) The energy of the third Balmer transition in $He^{\oplus}$ $(Z=2)$ corresponds to the transition from $n=5$ to $n=2$.$\Delta E = 13.6 	imes Z^{2} 	imes (\frac{1}{n_1^{2}} - \frac{1}{n_2^{2}}) = 13.6 	imes 4 	imes (\frac{1}{2^{2}} - \frac{1}{5^{2}}) = 54.4 	imes (0.25 - 0.04) = 54.4 	imes 0.21 = 11.424 \, eV$.$(A)$ First excitation energy of $He^{\oplus}$ ($n=1$ to $n=2$): $\Delta E = 13.6 	imes 4 	imes (1 - \frac{1}{4}) = 54.4 	imes 0.75 = 40.8 \, eV$.$(B)$ Third separation energy of $Li^{2+}$ $(Z=3)$ corresponds to $n=4$ to $n=\infty$: $\Delta E = 13.6 	imes 9 	imes (\frac{1}{4^{2}}) = 122.4 	imes 0.0625 = 7.65 \, eV$.$(C)$ Fourth excitation energy of $H$ atom ($n=1$ to $n=5$): $\Delta E = 13.6 	imes 1 	imes (1 - \frac{1}{25}) = 13.6 	imes 0.96 = 13.056 \, eV$.$(D)$ Ionisation energy of $Be^{3+}$ $(Z=4)$: $\Delta E = 13.6 	imes 16 = 217.6 \, eV$.Comparing the values,$7.65 \, eV < 11.424 \, eV$. Thus,option $B$ is correct.

Which of the following energy changes is less than the third Balmer transition in the $He^{\oplus}$ ion?

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