# A $He^{+}$ ion is in its first excited state . Its ionization energy is : Option 1) $48.36\:\:eV$ Option 2) $54.40\:\:eV$ Option 3) $13.60\:\:eV$ Option 4) $6.04\:\:eV$

we know that ,

$E_{n}=-13.6 \left ( \frac{Z^{2}}{n^{2}} \right )$

in first excited state for $He^{+}$

$\Rightarrow n=2,Z=2$

$E=-13.6\times\left ( \frac{2^{2}}{2^{2}} \right )=-13.6\:eV$

$\Rightarrow Ionisation\:\:\:energy=+13.6\:eV$

Option 1)

$48.36\:\:eV$

Option 2)

$54.40\:\:eV$

Option 3)

$13.60\:\:eV$

Option 4)

$6.04\:\:eV$

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