Question

current attempt in progress
how many s electrons, p electrons, and d electrons are possible in any energy level?
s orbital: electrons per shell
p orbital: electrons per shell after the 1st energy level
d orbital: electrons per shell after the 2nd energy level
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Explanation:

Step1: Determine the number of orbitals for each type

• For \(s\) orbitals: There is \(1\) \(s\) orbital (\(l = 0\), \(m_l=0\)).
• For \(p\) orbitals: There are \(3\) \(p\) orbitals (\(l = 1\), \(m_l=- 1,0,1\)).
• For \(d\) orbitals: There are \(5\) \(d\) orbitals (\(l = 2\), \(m_l=-2,-1,0,1,2\)).

Step2: Calculate the number of electrons using Pauli's exclusion principle

• Since each orbital can hold a maximum of \(2\) electrons (Pauli's exclusion principle: electrons in the same orbital must have opposite spins).
• For \(s\) orbitals: \(1\times2 = 2\) electrons.
• For \(p\) orbitals: \(3\times2=6\) electrons.
• For \(d\) orbitals: \(5\times2 = 10\) electrons.

Answer:

\(s\) orbital: \(2\) electrons per shell; \(p\) orbital: \(6\) electrons per shell after the \(1^{st}\) energy level; \(d\) orbital: \(10\) electrons per shell after the \(2^{nd}\) energy level.