Q.Calculate the energy equivalent of $1\ \text{g}$ of substance.

The key idea is mass-energy equivalence: mass can be converted into energy according to $E = mc^2$.

Step 1: Convert mass to kilograms.

$1\ \text{g} = 1 \times 10^{-3}\ \text{kg}$.

Step 2: Use $c = 3 \times 10^8\ \text{m/s}$.

$E = (1 \times 10^{-3}) \times (3 \times 10^8)^2$.

Step 3: Compute. …

The core idea here is Einstein's mass-energy equivalence — one of the most profound results in physics. It tells us that mass is not just a measure of inertia or gravitational pull; it is a concentrated form of energy. The relation $E = mc^2$ means that even a tiny amount of mass contains an enormous amount of energy because $c^2$ is a huge number ($c = 3 \times 10^8\ \text{m/s}$).

Why does this matter? In nuclear reactions (fission, fusion) or particle-antiparticle annihilation, a small fraction of mass converts into energy. The problem asks for the complete conversion of $1\ \text{g}$ — that is, all its mass turns into energy. This is the maximum possible energy you could extract from that mass.

Let's work through the calculation step by step.

1. Write down the formula The energy equivalent of mass $m$ is:

where $c = 3 \times 10^8\ \text{m/s}$ is the speed of light in vacuum.

2. Convert mass to SI units The mass is given as $1\ \text{g}$. In the SI system, the standard unit of mass is the kilogram. So:

3. Plug in the numbers

First square the speed of light:

Then multiply:

4. Interpret the result …

Method: Einstein's Mass-Energy Equivalence (Direct Formula)

The core idea is that mass and energy are two forms of the same thing, linked by the speed of light squared. For any amount of mass $m$, the equivalent energy $E$ is given by:

where $c = 3 \times 10^8\ \text{m/s}$ (the speed of light in vacuum).

Steps

Step 1: Convert mass to SI units.

The formula uses mass in kilograms.

$1\ \text{g} = 1 \times 10^{-3}\ \text{kg}$.

Step 2: Substitute into $E = mc^2$.

Step 3: Square the speed of light first.

Step 4: Multiply by mass. …

Common Mistakes with Mass–Energy Equivalence

The question "Calculate the energy equivalent of 1 g of substance" looks deceptively simple — and that's exactly where students slip up. Here are the most frequent errors and how to avoid each.

Mistake 1: Forgetting to convert grams to kilograms

$E = mc^2$ requires mass in kilograms, not grams. Using $m = 1$ instead of $m = 10^{-3}$ gives an answer that is 1000 times too large.

How to avoid: Before you write anything, convert every mass to kg. For 1 g, write $m = 1 \times 10^{-3}\ \text{kg}$ explicitly. Make it a habit: mass in kg first, then plug into $E = mc^2$.

Mistake 2: Using the wrong value of $c$

Some students use $c = 3 \times 10^8\ \text{m/s}$ (which is correct) but then square it incorrectly — either forgetting to square or squaring only the coefficient and not the power of ten.

How to avoid: Write $c^2$ step by step:

Do not skip this step. A common slip is writing $3 \times 10^{16}$ instead of $9 \times 10^{16}$.

Mistake 3: Getting the units wrong

The energy comes out in joules (J) when mass is in kg and $c$ in m/s. Some students report the answer in eV or forget to state units entirely.

How to avoid: Always write the unit after your numerical answer. For this problem, the answer is in joules. If the question asks for energy equivalent, the standard SI unit is the joule unless specified otherwise.

Mistake 4: Misplacing the decimal in the final calculation

Even with correct conversion and squaring, students often mess up the powers of ten when multiplying $10^{-3}$ by $9 \times 10^{16}$.

How to avoid: Do the powers of ten separately:

Then multiply by 9: $9 \times 10^{13}\ \text{J}$. Write this as a separate line — don't try to do it all in your head.

Mistake 5: Confusing mass defect with mass of a substance …