Question

the n = 1 energy level contains ________ p orbitals, while all other energy levels contain ______ p orbitals. 2, 6 0, 3 6, 2 3, 3 0, 4

Explanation:

In quantum mechanics, for a given principal quantum number \(n\), the angular - momentum quantum number \(l\) can take values from \(0\) to \(n - 1\). For \(p\) orbitals, \(l = 1\). When \(n=1\), \(l\) can only be \(0\) (s - orbital), so there are \(0\) \(p\) orbitals. For \(n\geq2\), when \(l = 1\) (p - orbital), the magnetic quantum number \(m_l\) can take values \(-l,-l + 1,\cdots,l\). When \(l = 1\), \(m_l=- 1,0,1\), so there are \(3\) \(p\) orbitals.

Answer:

0, 3