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Well, I would use to check these. I looked up the first two ionization energies (by typing the atomic symbol) and got...

  • $"IE"_1 ("N") = "14.534 eV"" "" "" ""IE"_1 ("O") = "13.618 eV"$
  • $"IE"_2 ("N") = "29.601 eV"" "" "" ""IE"_2 ("O") = "35.121 eV"$

or...

  • $"IE"_1 ("N") ~~ "1402 kJ/mol"" "" ""IE"_1 ("O") ~~ "1314 kJ/mol"$
  • $"IE"_2 ("N") ~~ "2856 kJ/mol"" "" ""IE"_2 ("O") ~~ "3389 kJ/mol"$

Here, you can see that the first ionization energy of oxygen atom is lower. Consider the electron configurations.

$"N": [He]2s^2 2p^3$

$underbrace(ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))" "ul(uarr color(white)(darr)))$
$" "" "" "color(white)(.)2p$
$ul(uarr darr)$
$color(white)(.)2s$

$"O": [He]2s^2 2p^4$

$underbrace(ul(uarr darr)" "ul(uarr color(white)(darr))" "ul(uarr color(white)(darr)))$
$" "" "" "color(white)(.)2p$
$ul(uarr darr)$
$color(white)(.)2s$

Since oxygen has a paired $2p$ electron, that one will repel the others, making it easier to remove than any of the others.

Easier to remove $->$ lower ionization energy.

The second ionization energy of oxygen is higher than for nitrogen. In principle, they should be the same for two seemingly identical $2p$ electrons, BUT we would neglect an important factor...

It is because oxygen atom is smaller due to a higher effective nuclear charge $Z_(eff) = Z - S$, where $S$ is approximated to be the number of core electrons and $Z$ is the .

$Z_(eff,N) ~~ "7 protons" - "2 core e"^(-) ~~ 5$
$Z_(eff,O) ~~ "8 protons" - "2 core e"^(-) ~~ 6$

So, it is more difficult to remove the electron from the smaller atom, whose electrons are more tightly bound to the nucleus.

Harder to remove $->$ higher ionization energy.

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