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: State Einstein's mass-energy relation.
The energy equivalent of a mass \(m\) is given by
\[ E = mc^2 \]
where \(c = 3 \times 10^{8}\ \text{m/s}\) is the speed of light.

Step 2: Convert the mass to SI units.
\[ m = 1.0\ \text{g} = 1.0 \times 10^{-3}\ \text{kg} \]

Step 3: Substitute the values.
\[ E = (1.0 \times 10^{-3}) \times (3 \times 10^{8})^2 \]

Step 4: Evaluate the square and multiply.
\[ (3 \times 10^{8})^2 = 9 \times 10^{16}\ \text{m}^2/\text{s}^2 \]
\[ E = (1.0 \times 10^{-3}) \times (9 \times 10^{16}) = 9 \times 10^{13}\ \text{J} \]

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