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  • How much energy is required to ionise a H atom if the electron occupies n = 5 orbit? Compare your answer with the ionization enthalpy of H atom (energy required to remove the electron from n = 1 orbit).

2.14  How much energy is required to ionise a H atom if the electron occupies n = 5 orbit? Compare your answer with the ionization enthalpy of H atom ( energy required to remove the electron from n =1 orbit).

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The energy which is required to ionize an H atom if the electron occupies n=5 orbit is:

E_{n} = \frac{-21.8\times10^{-19}}{n^2} J\ atom^{-1}

For ionization from 5th orbit, n_{1} = 5\ and\ n_{2} = \infty

Therefore, \triangle E = E_{2}-E_{1} =-21.8\times10^{-19}\times\left ( \frac{1}{n_{2}^2} - \frac{1}{n_{1}^2}\right ) = 21.8\times10^{-19}\times\left ( \frac{1}{n_{1}^2}-\frac{1}{n_{2}^2} \right )=21.8\times10^{-19}\times\left ( \frac{1}{5}^2 - \frac{1}{\infty} \right ) = 8.72\times10^{-20}J

For ionization from 1st orbit, n_{1} = 1\ and\ n_{2} = \infty

Therefore,

\triangle E' =21.8\times10^{-19}\times\left ( \frac{1}{1}^2 -\frac{1}{\infty} \right ) = 21.8\times10^{-19}J

\frac{\triangle E'}{\triangle E} = \frac{21.8\times10^{-19}}{8.72\times10^{-20}} = 25

Hence, 25 times less energy is required to ionize an electron in the 5th orbital of the hydrogen atom as compared to that in the ground state.

Posted by

Divya Prakash Singh

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