Question

in one atom, what is the maximum number of electrons that could have the quantum number of ( n = 2 )?

Explanation:

Step1: Determine the possible values of \( l \)

For \( n = 2 \), the possible values of the angular - momentum quantum number \( l \) are \( l=0\) and \( l = 1\).

Step2: Calculate the number of orbitals for each \( l \)

• When \( l = 0\) (s - orbital), the magnetic quantum number \( m_l=0\). So, there is \(1\) orbital.
• When \( l = 1\) (p - orbitals), \(m_l=- 1,0,1\). So, there are \(3\) orbitals.

The total number of orbitals for \(n = 2\) is \(1 + 3=4\).

Step3: Use the Pauli exclusion principle

According to the Pauli exclusion principle, each orbital can hold a maximum of \(2\) electrons.
If the number of orbitals is \(N = 4\), the number of electrons \(E=2N\).
Substitute \(N = 4\) into the formula \(E = 2N\), we get \(E=2\times4 = 8\).

Answer:

\(8\)