1 and 2 are the labels of two electrons. If ϕ1s and ϕ2s are the 1s and 2s wavefunctions of He atom and a and ẞ are the spin wavefunctions of an electron, the Slater determinant that correctly describes one of the symmetry-adapted excited states of He atom is
1
\(\rm \left|\begin{matrix}\phi_{1s}(1)\alpha(1)&\phi_{1s}(2)\alpha(2)\\\ \phi_{1s}(1)\beta(1)&\phi_{1s}(2)\beta(2) \end{matrix}\right|\)
2
\(\rm \left|\begin{matrix}\phi_{1s}(1)\alpha(1)&\phi_{1s}(2)\alpha(2)\\\ \phi_{2s}(1)\beta(1)&\phi_{2s}(2)\beta(2) \end{matrix}\right|\)
3
\(\rm \left|\begin{matrix}\phi_{1s}(1)\alpha(1)&\phi_{1s}(2)\alpha(2)\\\ \phi_{2s}(1)\alpha(1)&\phi_{2s}(2)\alpha(2) \end{matrix}\right|\)
4
\(\rm \left|\begin{matrix}\phi_{1s}(1)\beta(1)&\phi_{1s}(2)\beta(2)\\\ \phi_{2s}(1)\alpha(1)&\phi_{2s}(2)\alpha(2) \end{matrix}\right|\)