Question

Find out equivalent energy of 1·0 gm of a substance.

Hint:

Apply \(E = mc^2\) with the mass in kilograms; 1 gram is \(10^{-3}\) kg.

Answer 1

Step 1: Identify the principle.
Mass and energy are interconvertible; a mass \(m\) completely converted to energy yields \(E = mc^2\), from Einstein's special theory of relativity.

Step 2: Express the given mass in kilograms.
\(1.0\ \text{gm} = 10^{-3}\ \text{kg}\).

Step 3: Write \(c^2\).
With \(c = 3 \times 10^{8}\ \text{m/s}\), \(c^2 = 9 \times 10^{16}\ \text{m}^2\text{s}^{-2}\).

Step 4: Multiply mass by \(c^2\).
\(E = 10^{-3} \times 9 \times 10^{16} = 9 \times 10^{13}\ \text{J}\).

Step 5: Interpret.
Just one gram of matter, if fully converted, releases \(9 \times 10^{13}\) joules, an enormous amount of energy, which is why nuclear reactions are so powerful.

\[\boxed{E = 9 \times 10^{13}\ \text{J}}\]