Question

the ionization energy of hydrogen atom is 13.6 electron volt the energy required to excite the electron in a hydrogen atom from the ground state to the first excited state is

Answer 1

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Answer 2

Answer: The energy required to excite an electron from ground state to first excited state is 10.2 eV.

Explanation:

Ionization energy is defined as the energy which is released when a valence electron is ejected out of an isolated gaseous atom.

The formula used to calculate ionization energy follows:

$E_n=\frac{-E_o\times Z^2}{n^2}eV$

where,

$E_o$ = energy of the ground state

Z = atomic number  = 1 (for hydrogen)

n = Energy level

The transition of ionization energy is from $1\rightarrow \infty$

We are given:

$13.6=(\frac{-E_o\times Z^2}{\infty ^2})-(\frac{-E_o\times 1^2}{1^2})\\\\E_o=-13.6eV$

Now, if the transition is from $1\rightarrow 2$

$E_n=(\frac{-13.6\times 1^2}{2^2})-(\frac{-13.6\times 1^2}{1^2})\\\\E_n=(-3.4+13.6)eV=10.2eV$

Hence, the energy required to excite an electron from ground state to first excited state is 10.2 eV.