Question

Question was provided via image upload.

Explanation:

Step1: Sulfur (S, Z=16)

Quantum Numbers (valence e⁻: 3s²3p⁴; take a 3p e⁻)

$n=3$ (principal shell), $l=1$ (p orbital), $m_l=+1$ (pₓ orbital), $m_s=+\frac{1}{2}$ (spin up)

Orbital Diagram (valence e⁻):

$$\begin{array}{ccc} \boxed{\uparrow\downarrow} & \boxed{\uparrow\phantom{\downarrow}} & \boxed{\uparrow\phantom{\downarrow}} \\ 3s & 3p_x & 3p_y & 3p_z \end{array}$$

Electron Configuration:

$1s^22s^22p^63s^23p^4$ or $[Ne]3s^23p^4$

Step2: Calcium (Ca, Z=20)

Quantum Numbers (valence e⁻: 4s²; take a 4s e⁻)

$n=4$, $l=0$ (s orbital), $m_l=0$, $m_s=+\frac{1}{2}$

Orbital Diagram (valence e⁻):

$$\begin{array}{c} \boxed{\uparrow\downarrow} \\ 4s \end{array}$$

Electron Configuration:

$1s^22s^22p^63s^23p^64s^2$ or $[Ar]4s^2$

Step3: Strontium (Sr, Z=38)

Quantum Numbers (valence e⁻: 5s²; take a 5s e⁻)

$n=5$, $l=0$, $m_l=0$, $m_s=+\frac{1}{2}$

Orbital Diagram (valence e⁻):

$$\begin{array}{c} \boxed{\uparrow\downarrow} \\ 5s \end{array}$$

Electron Configuration:

$1s^22s^22p^63s^23p^63d^{10}4s^24p^65s^2$ or $[Kr]5s^2$

Step4: Zinc (Zn, Z=30)

Quantum Numbers (valence e⁻: 4s²3d¹⁰; take a 3d e⁻)

$n=3$, $l=2$ (d orbital), $m_l=0$, $m_s=+\frac{1}{2}$

Orbital Diagram (valence e⁻):

$$\begin{array}{c} \boxed{\uparrow\downarrow} \\ 4s \end{array} \quad \begin{array}{ccccc} \boxed{\uparrow\downarrow} & \boxed{\uparrow\downarrow} & \boxed{\uparrow\downarrow} & \boxed{\uparrow\downarrow} & \boxed{\uparrow\downarrow} \\ 3d_{xy} & 3d_{xz} & 3d_{yz} & 3d_{x^2-y^2} & 3d_{z^2} \end{array}$$

Electron Configuration:

$1s^22s^22p^63s^23p^63d^{10}4s^2$ or $[Ar]3d^{10}4s^2$

Step5: Cadmium (Cd, Z=48)

Quantum Numbers (valence e⁻: 5s²4d¹⁰; take a 4d e⁻)

$n=4$, $l=2$, $m_l=0$, $m_s=+\frac{1}{2}$

Orbital Diagram (valence e⁻):

$$\begin{array}{c} \boxed{\uparrow\downarrow} \\ 5s \end{array} \quad \begin{array}{ccccc} \boxed{\uparrow\downarrow} & \boxed{\uparrow\downarrow} & \boxed{\uparrow\downarrow} & \boxed{\uparrow\downarrow} & \boxed{\uparrow\downarrow} \\ 4d_{xy} & 4d_{xz} & 4d_{yz} & 4d_{x^2-y^2} & 4d_{z^2} \end{array}$$

Electron Configuration:

$1s^22s^22p^63s^23p^63d^{10}4s^24p^64d^{10}5s^2$ or $[Kr]4d^{10}5s^2$

Step6: Practice (Ground State Configurations)

Scandium (Sc, Z=21):

Fill orbitals by Aufbau principle: $[Ar]3d^14s^2$

Iron (Fe, Z=26):

Half-fill d orbitals first: $[Ar]3d^64s^2$

Gallium (Ga, Z=31):

Post-transition metal: $[Ar]3d^{10}4s^24p^1$

Cadmium (Cd, Z=48):

As above: $[Kr]4d^{10}5s^2$

Lead (Pb, Z=82):

Post-transition metal: $[Xe]4f^{14}5d^{10}6s^26p^2$

Tennessine (Ts, Z=117):

Halogens, 7th period: $[Rn]5f^{14}6d^{10}7s^27p^5$

Answer:

Completed Table:

Element	Quantum Numbers (for one valence e⁻)	Orbital diagram of valence electrons	Electron configuration

$$\begin{array}{c}\boxed{\uparrow\downarrow} \\ 3s\end{array}\quad\begin{array}{ccc}\boxed{\uparrow\phantom{\downarrow}}&\boxed{\uparrow\phantom{\downarrow}}&\boxed{\uparrow\downarrow}\end{array}$$

<br> $3p_x\quad3p_y\quad3p_z$ | $[Ne]3s^23p^4$ |

Calcium

$n=4, l=0, m_l=0, m_s=+\frac{1}{2}$

$$\begin{array}{c}\boxed{\uparrow\downarrow} \\ 4s\end{array}$$

| $[Ar]4s^2$ |

Strontium

$n=5, l=0, m_l=0, m_s=+\frac{1}{2}$

$$\begin{array}{c}\boxed{\uparrow\downarrow} \\ 5s\end{array}$$

| $[Kr]5s^2$ |

Zinc	$n=3, l=2, m_l=0, m_s=+\frac{1}{2}$

$$\begin{array}{c}\boxed{\uparrow\downarrow} \\ 4s\end{array}\quad\begin{array}{ccccc}\boxed{\uparrow\downarrow}&\boxed{\uparrow\downarrow}&\boxed{\uparrow\downarrow}&\boxed{\uparrow\downarrow}&\boxed{\uparrow\downarrow}\end{array}$$

<br> $3d_{xy}\quad3d_{xz}\quad3d_{yz}\quad3d_{x^2-y^2}\quad3d_{z^2}$ | $[Ar]3d^{10}4s^2$ |

Cadmium

$n=4, l=2, m_l=0, m_s=+\frac{1}{2}$

$$\begin{array}{c}\boxed{\uparrow\downarrow} \\ 5s\end{array}\quad\begin{array}{ccccc}\boxed{\uparrow\downarrow}&\boxed{\uparrow\downarrow}&\boxed{\uparrow\downarrow}&\boxed{\uparrow\downarrow}&\boxed{\uparrow\downarrow}\end{array}$$

<br> $4d_{xy}\quad4d_{xz}\quad4d_{yz}\quad4d_{x^2-y^2}\quad4d_{z^2}$ | $[Kr]4d^{10}5s^2$ |

Practice Answers:

• Scandium: $[Ar]3d^14s^2$
• Iron: $[Ar]3d^64s^2$
• Gallium: $[Ar]3d^{10}4s^24p^1$
• Cadmium: $[Kr]4d^{10}5s^2$
• Lead: $[Xe]4f^{14}5d^{10}6s^26p^2$
• Tennessine: $[Rn]5f^{14}6d^{10}7s^27p^5$