Question

The energy equivalent of 0.5 g of a substance is:

• A. $4.5 \times 10^{16} J$
• B. $4.5 \times 10^{13} J$
• C. $1.5 \times 10^{13} J$
• D. $0.5 \times 10^{13} J$

Answer 1

The Correct Option is B

To find the energy equivalent of a mass, we use Einstein's mass-energy equivalence principle, expressed by the famous equation:

\(E = mc^2\)

where:

• \(E\) is the energy.
• \(m\) is the mass.
• \(c\) is the speed of light in vacuum, approximately \(3 \times 10^8 \, \text{m/s}\).

We need to find the energy equivalent of \(0.5 \, \text{g}\) of a substance. First, convert the mass from grams to kilograms, because the SI unit of mass is kilograms.

\(0.5 \, \text{g} = 0.5 \times 10^{-3} \, \text{kg}\)

Substitute the values into the mass-energy equivalence formula:

\(E = (0.5 \times 10^{-3} \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2\)

\(E = 0.5 \times 10^{-3} \times 9 \times 10^{16} \, \text{J}\)

\(E = 4.5 \times 10^{13} \, \text{J}\)

Hence, the energy equivalent of \(0.5 \, \text{g}\) of the substance is \(4.5 \times 10^{13} \, \text{J}\).

Therefore, the correct answer is:

• \(4.5 \times 10^{13} \, \text{J}\)