How many unpaired electrons are contained in each element: (a) calcium, (b) argon, (c) aluminum, and (d) carbon?

Unpaired electrons are those electrons which exist singly in orbital, without making pair with other electron

CALCIUM:

Atomic Number 20

Electronic Configuration;  1s², 2s², 2p⁶, 3s², 3p⁶, 4s²

Number of Unpaired e⁻s; Zero

ARGON:

Atomic Number 18

Electronic Configuration;  1s², 2s², 2p⁶, 3s², 3p⁶

Number of Unpaired e⁻s; Zero

ALUMINIUM:

Atomic Number 13

Electronic Configuration;  1s², 2s², 2p⁶, 3s², 3p¹                (Ground State)
Electronic Configuration;  1s², 2s², 2p⁶, 3s¹, 3px¹, 3py¹     (Excited State)

Number of Unpaired e⁻s; 1 in Ground state and 3 in Excited State.

CARBON:

Atomic Number 6

Electronic Configuration;  1s², 2s², 2px¹, 2py¹               (Ground State)
Electronic Configuration;  1s², 2s¹, 2px¹, 2py¹, 2pz¹      (Excited State)

Number of Unpaired e⁻s; 2 in Ground state and 4 in Excited State

The activity series is shown in the attached picture. if the element is below the other, then you can displace the other. following the activity series as a guide, the reactions are as follows: nickel and aluminum chloride3 ni + 2 alcl₃  → 3 nicl₂ + 2 albarium and copper bromideba + cubr  →  no reaction because cu is less oxidizable than bapotassium nitrate and aluminum3 kno₃ + al  → al(no₃)₃ + 3 ksodium phosphate and zincnaso₄ + zn  → znso₄ + na