Which of the following equations are correctly balanced?

$\bold{A.} \quad \phantom{X}^{q-1}${p-5}X \longrightarrow \phantom{X}^{q-5}{p-3}Y + \phantom{X}^{4}{2}He \\[1em] \bold{B.} \quad \phantom{X}^{q-4}{p-4}Z \longrightarrow \phantom{X}^{q-4}{p-5}X + \phantom{X}^{\phantom{1}0}{-1}e \\[1em] \bold{C.} \quad \phantom{X}^{q-1}{p-5}X \longrightarrow \phantom{X}^{q-5}{p-7}Y + \phantom{X}^{4}{2}He \\[1em] \bold{D.} \quad \phantom{X}^{q-4}{p-7}Z \longrightarrow \phantom{X}^{q-4}{p-5}X + \phantom{X}2^{\phantom{1}0}{-1}e \\[1em]

1. Only D
2. Only C
3. Both A & B
4. Both C & D

Both C & D

Reason — A balanced nuclear equation must conserve:

• Mass number (top value) — total nucleons (protons + neutrons)
• Atomic number (bottom value) — total protons

Equation A
LHS: Mass number= q-1
Atomic number = p-5
RHS: mass number= (q-5 + 4) = q-1
Atomic number= (p-3 + 2) = p-1
so this equation is not balanced.

Equation B
LHS: Mass number= q-4
Atomic number = p-4
RHS: mass number= (q-4 + 0) = q-4
Atomic number= p-5 + (-1) = p-6
so this equation is not balanced.

Equation C
LHS: Mass number= q-1
Atomic number = p-5
RHS: mass number= (q-5 + 4) = q-1
Atomic number= (p-7 + 2) = p-5
so this equation is balanced.

Equation D
LHS: Mass number= q-4
Atomic number= p-7
RHS: Mass number= q-4 + 0 = q-4
Atomic number= p-5 + 2(-1) = p-7
so this equation is balanced.