Question

The energy equivalent of 1g of substance is:

• A. \( 11.2 \times 10^{24} \, \text{MeV} \)
• B. \( 5.6 \times 10^{12} \, \text{MeV} \)
• C. \( 5.6 \, \text{eV} \)
• D. \( 5.6 \times 10^{26} \, \text{MeV} \)

Answer 1

The Correct Option is D

The energy equivalent of 1 gram of a substance is determined using Einstein's mass-energy equivalence principle, defined by the equation:

\(E = mc^2\)

where:

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

For 1 gram of substance:

• \(m = 1 \, \text{g} = 1 \times 10^{-3} \, \text{kg}\).

Substituting these values into the equation yields:

\(E = (1 \times 10^{-3} \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2\)

The value inside the parentheses calculates to:

\((3 \times 10^8 \, \text{m/s})^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2\)

Multiplying these values gives:

\(E = (1 \times 10^{-3}) \times (9 \times 10^{16})\)

\(E = 9 \times 10^{13} \, \text{joules}\)

To convert joules to electronvolts (eV), the conversion factor is:

\(1 \, \text{joule} = 6.242 \times 10^{18} \, \text{eV}\)

Therefore:

\(E = 9 \times 10^{13} \, \text{joules} \times 6.242 \times 10^{18} \, \text{eV/joule}\)

\(E = 5.6178 \times 10^{32} \, \text{eV}\)

Converting electronvolts to mega-electronvolts (MeV) uses the relation:

\(1 \, \text{MeV} = 10^6 \, \text{eV}\)

\(E = \frac{5.6178 \times 10^{32} \, \text{eV}}{10^6}\)

\(E = 5.6178 \times 10^{26} \, \text{MeV}\)

The energy equivalent of 1 g of substance is approximately \(5.6 \times 10^{26} \, \text{MeV}\).