Q.Answer the following questions:

(a) Balancing of nuclear vs. chemical equations

A chemical equation balances atoms — the same number of each element on both sides. A nuclear reaction equation balances nucleons (protons + neutrons) and charge (proton number). It does not balance the number of atoms or molecules; instead, it shows the transformation of one nucleus into another.

(b) How mass converts to energy if nucleons are conserved

Even though the total number of nucleons is conserved, the total mass of the products is slightly less than the total mass of the reactants. This mass difference ($\Delta m$) is converted into energy via $E = \Delta m \, c^2$. The missing mass appears as kinetic energy of the products or as gamma radiation.

(c) Mass-energy conversion in chemical reactions …

(a) Balancing in nuclear vs. chemical equations

A chemical equation like $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ balances atoms and charge — the same number of each element appears on both sides. The molecules themselves rearrange, but the atoms are conserved.

A nuclear reaction equation, such as

does not balance in the chemical sense — the elements on the left and right are different. Nitrogen and helium become oxygen and hydrogen. What is conserved are two quantities:

1. Mass number (nucleon number) — the superscripts: $14 + 4 = 17 + 1$
2. Atomic number (proton number / charge) — the subscripts: $7 + 2 = 8 + 1$

So a nuclear equation is balanced in terms of total nucleons and total charge, not in terms of chemical species. The identity of the nucleus changes, but the building blocks (protons and neutrons) are simply rearranged.

(b) If nucleons are conserved, where does the energy come from?

If the number of protons and neutrons is the same on both sides, you might wonder: how can mass be converted into energy? The key is that the total mass of the separated nucleons is not the same as the mass of the nucleus they form.

A nucleus is held together by the strong nuclear force. To pull it apart into individual protons and neutrons, you must supply energy — this energy is stored as the binding energy of the nucleus. Conversely, when nucleons fuse, they release that binding energy.

Because of Einstein’s relation $E = mc^2$, this binding energy corresponds to a mass defect:

where $\Delta m > 0$ for a stable nucleus. The mass of the nucleus is less than the sum of the masses of its constituents.

In a nuclear reaction, the total number of nucleons is conserved, but the binding energy per nucleon differs between the reactants and products. If the products have a higher binding energy per nucleon (i.e., they are more tightly bound), the total mass of the products is slightly less than that of the reactants. The missing mass appears as kinetic energy of the products (or as gamma radiation), according to $E = \Delta m \, c^2$.

So mass is not "destroyed" — it is converted into energy, and the nucleon count remains unchanged. The mass defect is a measure of the binding energy difference.

(c) Mass-energy interconversion in chemical reactions

It is a widespread misconception that $E=mc^2$ only matters in nuclear physics. In truth, every exothermic chemical reaction also involves a tiny mass decrease.

When hydrogen burns:

$2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O} + \text{energy}$ …

Method: Conservation Laws in Nuclear Reaction Balancing

The method is Conservation of Nucleon Number and Charge. Unlike chemical equations, nuclear reactions are not balanced by conserving atoms or molecules — they are balanced by conserving two fundamental quantities on each side of the arrow.

Steps

1. Check conservation of mass number (A) — the total number of nucleons (protons + neutrons) must be the same on both sides.
2. Check conservation of atomic number (Z) — the total charge (number of protons) must be the same on both sides.
3. Check that the resulting nuclide is physically possible — the product must have a known isotope with the calculated Z and A.

(a) How are nuclear equations "balanced"?

No, nuclear equations are not balanced in the chemical sense. A chemical equation like $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ is balanced by conserving the number of atoms of each element — the same atoms rearrange, nothing changes identity at the nuclear level.

A nuclear equation is balanced by conserving nucleon count and charge. The identities of elements can change completely. For example, in alpha decay:

Left: A = 238, Z = 92. Right: A = 234 + 4 = 238, Z = 90 + 2 = 92. The numbers match, but uranium has become thorium plus helium — atoms are not "preserved" the way they are in chemistry.

(b) If nucleons are conserved, where does the mass-energy conversion come from?

The number of nucleons is conserved, but the total mass of the products is slightly less than the total mass of the reactants. This mass difference ($\Delta m$) is converted into energy via $E = \Delta m c^2$.

Why does mass decrease even though the count of protons and neutrons stays the same? Because the binding energy per nucleon differs between the initial and final nuclei. A nucleus with higher binding energy per nucleon is more tightly bound and has less mass per nucleon. The "missing" mass is the mass equivalent of the binding energy released.

(c) Mass-energy conversion also occurs in chemical reactions — why the impression is incorrect …

Common Mistakes in Nuclear Reaction Balancing

Mistake 1: Treating nuclear equations like chemical equations

Students often try to balance nuclear reactions by matching the number of atoms of each element on both sides, just as they would for $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$.

Why this fails: In a chemical equation, atoms are conserved — the same elements appear on both sides. In a nuclear reaction, elements can change because the nucleus itself transforms. A uranium nucleus splitting into barium and krypton doesn't have "equal uranium atoms" on both sides.

How to avoid: Instead of looking at elements, look at two numbers only:

• Mass number (A) — the superscript (total protons + neutrons)
• Atomic number (Z) — the subscript (number of protons)

Both A and Z must sum to the same total on left and right. That's the only balancing that matters.

Mistake 2: Forgetting that mass-energy conversion happens within conserved totals

This connects directly to part (b) of your question. Students see that the total number of protons and neutrons is conserved and then wonder: where does the energy come from?

The confusion: If 92 protons and 143 neutrons go in, and 92 protons and 143 neutrons come out, how can mass have been converted to energy?

The resolution: The count of nucleons is conserved, but the total mass of the nucleus is not equal to the sum of the masses of its individual protons and neutrons. The mass of a nucleus is less than the sum of its parts — that difference is the mass defect, which corresponds to binding energy.

When a nuclear reaction releases energy, the total mass of the products is slightly less than the total mass of the reactants, even though the number of protons and neutrons is identical. That missing mass has become energy via $E = mc^2$.

Mistake 3: Believing mass-energy conversion is exclusive to nuclear reactions

This addresses part (c). Many students think chemical reactions involve only energy rearrangement, with no mass change at all.

The error: Chemical reactions do involve mass-energy conversion — the effect is just too tiny to measure. When hydrogen burns:

The reaction releases about $286\ \text{kJ/mol}$ of energy. Using $E = mc^2$, the corresponding mass change is:

That's roughly one part in $10^{10}$ of the total mass — far below the sensitivity of any chemical balance. …