Answer
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The lowest value of \( n \) for which \( g \) orbitals could exist can be determined using the relationship between the principal quantum number \( n \) and the azimuthal quantum number \( \ell \). The azimuthal quantum number \( \ell \) for \( g \) orbitals is 4. According to the relationship \( \ell \) can range from 0 to \( n-1 \). Therefore, the lowest value of \( n \) for which \( g \) orbitals could exist is \( n = 5 \).
The possible values of \( m_{\ell} \) for \( g \) orbitals can be calculated using the formula \( m_{\ell} = -\ell, -\ell + 1, ..., 0, ..., \ell - 1, \ell \). For \( \ell = 4 \), the possible values of \( m_{\ell} \) are -4, -3, -2, -1, 0, 1, 2, 3, 4.
The maximum number of electrons that can occupy a set of \( g \) orbitals can be determined using the formula \( 2(2\ell + 1) \). For \( \ell = 4 \), the maximum number of electrons that could occupy a set of \( g \) orbitals is \( 2(2(4) + 1) = 18 \) electrons.
