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Question

The ionisation potential of hydrogen atom is $$13.6\ eV$$. The energy required to remove an electrons in the $$n=2$$ state of hydrogen atom is:

A
$$13.6\ eV$$
B
$$27.2\ eV$$
C
$$6.8\ eV$$
D
$$3.4\ eV$$
Solution
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Correct option is D. $$3.4\ eV$$
$$E_n=-13.6\ ev\left (\dfrac {Z^2}{n^2}\right)=\dfrac {-E_1}{n^2}[I.E_1 =-E_1 =13.6\ eV \Rightarrow E_1=-13.6\ eV]$$

$$\therefore E_2 =\dfrac {-13.6\ ev}{4}=-3.4ev$$

$$\therefore I.E_2=-E_2 =3.4\ ev$$.

Option D is correct.

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