The correct increasing order for second ionization energy of $He,Li,Be,B,C,N,O,F,Ne$ is :

The correct option is B $Be<C<B<N<F<O<Ne<He<Li$
$H{e}^{+}-1s^1$
$L{i}^{+}-\left[He\right]$
$B{e}^{+}-\left[He\right]2s^1$
$B^{+}-\left[He\right]2s^2$
$C^{+}-\left[He\right]2s^{2}2p^1$
$N^{+}-\left[He\right]2s^{2}2p^2$
$O^{+}-\left[He\right]2s^{2}2p^3$
$F^{+}-\left[He\right]2s^{2}2p^4$
$N{e}^{+}-\left[He\right]2s^{2}2p^5$
$L{i}^{+}$ is most stable and then comes $H{e}^{+}$. Half filled orbitals are more stable than partially filled.
Hence the correct order will be $Be<C<B<N<F<O<Ne<He<Li$