Electron Shell Conceptual Questions?

Question

INTRO:

Consider an electron in the state n = 4, l = 3, m = 2, s = 1/2.

QUESTIONS:

1) In what shell is this electron located?

2) In what subshell is this electron located?

3) How many other electrons could occupy the same subshell as this electron?

4) What is the orbital angular momentum L of this electron?

= ______ h (h bar)

5) What is the z component of the orbital angular momentum of this electron, L sub z?

= ______ h

6) What is the z component of the spin angular momentum of this electron, S sub z?

= ______ h

Answer 1

1)

The shell is given by the principal quantum number n.

So electron is in fourth shell. In notation of the classic shell model it is the N-shell

2)

Subshell is given by the azimuthal quantum number l.

l=3 stand for subshellf or f-orbital

3)

13, because there are up to 14 electron in a f-orbital.

Genral the total number of electron in subshell l is

z =4l + 2

4)

L² = l∙(l+1)∙ħ² = 12∙ħ²

=>

L = √12 ∙ ħ

5)

Lz = m ∙ ħ = 2 ∙ ħ

6)

Sz = s∙ħ = (1/2) ∙ ħ