Why Are There More Energy Levels in Silicon's 3p4p Configuration Than in 3p²?

[Matt atkinson]

Homework Statement

Silicon has the configuration [Mg] $3p^2$.
Explain why there are more L, S, J levels for the $3p4p$ configuration
than in the $3p^2$ configuration.

Homework Equations

The Attempt at a Solution

My thought is because in the $3p^2$ subshell you have less variations of $M_l$ and $M_s$ because both electrons cannot have the same quantum numbers, wheres with the $3p4p$ level, they could both have $M_l=+1$ and $M_s=+1$ because the $n$ the principle quantum number is different?

 

[DrClaude]

My thought is because in the $3p^2$ subshell you have less variations of $M_l$ and $M_s$ because both electrons cannot have the same quantum numbers, wheres with the $3p4p$ level, they could both have $M_l=+1$ and $M_s=+1$ because the $n$ the principle quantum number is different?

You're on the right track. But there are more states than just the one you cited ($M_l=+1$ and $M_s=+1$).

 

[Matt atkinson]

Yes, i understand that there would twice (?) as many states in the excited level because the electrons would be free to have any $m_l$ or $m_s$, but the states for the $3p^2$ level are restricted by the Pauli principle.

 

[DrClaude]

Yes, i understand that there would twice (?) as many states in the excited level because the electrons would be free to have any $m_l$ or $m_s$, but the states for the $3p^2$ level are restricted by the Pauli principle.

Not twice, because it is only the states where the two electrons have the same spin in the same orbital that have to be discarted. But I think you get the idea.

 

[Matt atkinson]

Ah okay thankyou!