Sum

(a) Find the first excitation potential of He^{+} ion. (b) Find the ionization potential of Li^{++}ion.

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#### Solution

(a) PE of hydrogen like atom in the *n*th state, V = `(-13.6Z^2)/n^2 eV`

Here, *Z* is the atomic number of that atom.

For the first excitation, the atom has to be excited from n = 1 to n = 2 state.

So, its excitation potential will be equal to the difference in the potential of the atom in n = 1 and in n = 2 states.

First excitation potential of He^{+}

`- 13.6Z^2 (1 - 1/2^2) eV`

= `- 10.2 Z^2 eV `

`rArr 10.2 xx Z^2 `

`= 10.2 xx 4`

= 40.8 (b) Ionization Potential Li^{++} = 13.6 V ×Z^{2}

= 13.6 × 9

= 122.4 V

Concept: The Line Spectra of the Hydrogen Atom

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