# If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is Option 1) 10.2 eV Option 2) 0 eV Option 3) 3.4 eV Option 4) 6.8 eV

P perimeter

As we learnt in

Ionization energy -

$E_{ion }= E_{\infty }-E_{n }$

$=13.6\frac{Z^{2}}{n^{2}}$

- wherein

Energy required to move an electron from ground state to $n= \infty$

$\Delta E =E_{0}z^{2}\left(\frac{1}{n_{i}^{2}}-\frac{1}{n_{f}^{2}} \right )$

For an electron to remove from

n = 2

ni = 2

$n_{f}\rightarrow \infty$

$E_{0}=13.6\ eV$     &    z = 1

$\therefore\ \; \Delta E=13.6\left(\frac{1}{4} \right )=3.4\ eV$

Correct option is 3.

Option 1)

10.2 eV

This is an incorrect option.

Option 2)

0 eV

This is an incorrect option.

Option 3)

3.4 eV

This is the correct option.

Option 4)

6.8 eV

This is an incorrect option.

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