Question

quantum numbers
write the four quantum numbers (n,l,m,m) for each circled electron in the diagram.
name tony xiong

electron a
electron b
electron c
electron d
electron e
electron f
electron g
electron h
electron i
electron j
electron k
electron l
electron m

n = principal energy level = 1, 2, 3, 4, 5, 6, 7
l = sublevel = s=0, p=1, d=2, f=3
ml = orbital sublevel = s = 0; p = -1, 0, +1; d = -2, -1, 0, +1, +2; f = -3, -2, -1, 0, +1, +2, +3
ms = magnetic spin = +1/2 or -1/2

Explanation:

Electron A

Step1: Determine \(n\)

The principal energy level \(n = 2\) (from \(2s\) orbital).

Step2: Determine \(l\)

For \(s\) - orbital, \(l=0\).

Step3: Determine \(m_l\)

For \(s\) - orbital (\(l = 0\)), \(m_l=0\).

Step4: Determine \(m_s\)

The spin is \(-\frac{1}{2}\) (down - arrow).
So, \((n,l,m_l,m_s)=(2,0,0,-\frac{1}{2})\)

Electron B

Step1: Determine \(n\)

The principal energy level \(n = 2\) (from \(2p\) orbital).

Step2: Determine \(l\)

For \(p\) - orbital, \(l = 1\).

Step3: Determine \(m_l\)

The first \(p\) - orbital (\(m_l=- 1\)).

Step4: Determine \(m_s\)

The spin is \(-\frac{1}{2}\) (down - arrow).
So, \((n,l,m_l,m_s)=(2,1,-1,-\frac{1}{2})\)

Electron C

Step1: Determine \(n\)

The principal energy level \(n = 4\) (from \(4s\) orbital).

Step2: Determine \(l\)

For \(s\) - orbital, \(l=0\).

Step3: Determine \(m_l\)

For \(s\) - orbital (\(l = 0\)), \(m_l=0\).

Step4: Determine \(m_s\)

The spin is \(+\frac{1}{2}\) (up - arrow).
So, \((n,l,m_l,m_s)=(4,0,0,+\frac{1}{2})\)

Electron D

Step1: Determine \(n\)

The principal energy level \(n = 3\) (from \(3d\) orbital).

Step2: Determine \(l\)

For \(d\) - orbital, \(l = 2\).

Step3: Determine \(m_l\)

The fifth \(d\) - orbital (\(m_l = + 2\)).

Step4: Determine \(m_s\)

The spin is \(-\frac{1}{2}\) (down - arrow).
So, \((n,l,m_l,m_s)=(3,2,+2,-\frac{1}{2})\)

Electron E

Step1: Determine \(n\)

The principal energy level \(n = 4\) (from \(4p\) orbital).

Step2: Determine \(l\)

For \(p\) - orbital, \(l = 1\).

Step3: Determine \(m_l\)

The first \(p\) - orbital (\(m_l=-1\)).

Step4: Determine \(m_s\)

The spin is \(-\frac{1}{2}\) (down - arrow).
So, \((n,l,m_l,m_s)=(4,1,-1,-\frac{1}{2})\)

Electron F

Step1: Determine \(n\)

The principal energy level \(n = 4\) (from \(4d\) orbital).

Step2: Determine \(l\)

For \(d\) - orbital, \(l = 2\).

Step3: Determine \(m_l\)

The fourth \(d\) - orbital (\(m_l=+1\)).

Step4: Determine \(m_s\)

The spin is \(-\frac{1}{2}\) (down - arrow).
So, \((n,l,m_l,m_s)=(4,2,+1,-\frac{1}{2})\)

Electron G

Step1: Determine \(n\)

The principal energy level \(n = 6\) (from \(6s\) orbital).

Step2: Determine \(l\)

For \(s\) - orbital, \(l=0\).

Step3: Determine \(m_l\)

For \(s\) - orbital (\(l = 0\)), \(m_l=0\).

Step4: Determine \(m_s\)

The spin is \(-\frac{1}{2}\) (down - arrow).
So, \((n,l,m_l,m_s)=(6,0,0,-\frac{1}{2})\)

Electron J

Step1: Determine \(n\)

The principal energy level \(n = 5\) (from \(5f\) orbital).

Step2: Determine \(l\)

For \(f\) - orbital, \(l = 3\).

Step3: Determine \(m_l\)

The first \(f\) - orbital (\(m_l=-3\)).

Step4: Determine \(m_s\)

The spin is \(+\frac{1}{2}\) (up - arrow).
So, \((n,l,m_l,m_s)=(5,3,-3,+\frac{1}{2})\)

Electron K

Step1: Determine \(n\)

The principal energy level \(n = 5\) (from \(5f\) orbital).

Step2: Determine \(l\)

For \(f\) - orbital, \(l = 3\).

Step3: Determine \(m_l\)

The first \(f\) - orbital (\(m_l=-3\)).

Step4: Determine \(m_s\)

The spin is \(-\frac{1}{2}\) (down - arrow).
So, \((n,l,m_l,m_s)=(5,3,-3,-\frac{1}{2})\)

Electron L

Step1: Determine \(n\)

The principal energy level \(n = 6\) (from \(6d\) orbital).

Step2: Determine \(l\)

For \(d\) - orbital, \(l = 2\).

Step3: Determine \(m_l\)

The second \(d\) - orbital (\(m_l=-1\)).

Step4: Determine \(m_s\)

The spin is \(-\frac{1}{2}\) (down - arrow).
So, \((n,l,m_l,m_s)=(6,2,-1,-\frac{1}{2})\)

Electron M

Step1: Determine \(n\)

The principal energy level \(n = 7\) (from \(7p\) orbital).

Step2: Determine \(l\)

For \(p\) - orbital, \(l = 1\).

Step3: Determine \(m_l\)

The second \(p\) - orbital (\(m_l = 0\)).

Step4: Determine \(m_s\)

The spin is \(-\frac{1}{2}\) (down - arrow).
So, \((n,l,m_l,m_s)=(7,1,0,-\frac{1}{2})\)

Answer:

Electron A: \((2,0,0,-\frac{1}{2})\)
Electron B: \((2,1,-1,-\frac{1}{2})\)
Electron C: \((4,0,0,+\frac{1}{2})\)
Electron D: \((3,2,+2,-\frac{1}{2})\)
Electron E: \((4,1,-1,-\frac{1}{2})\)
Electron F: \((4,2,+1,-\frac{1}{2})\)
Electron G: \((6,0,0,-\frac{1}{2})\)
Electron J: \((5,3,-3,+\frac{1}{2})\)
Electron K: \((5,3,-3,-\frac{1}{2})\)
Electron L: \((6,2,-1,-\frac{1}{2})\)
Electron M: \((7,1,0,-\frac{1}{2})\)