Question

The energy equivalent of one atomic mass unit is

• A. $1.6 \times 10^{-19} J$
• B. $6.02 \times 10^{-23} J$
• C. 931 MeV
• D. 9.31 MeV

Answer 1

The Correct Option is C

The question asks for the energy equivalent of one atomic mass unit (amu). This can be determined using 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 a vacuum, approximately 3 \times 10^8 \text{ m/s}.

An atomic mass unit is defined as 1/12th of the mass of a carbon-12 atom, and it approximately equals 1.66053906660 \times 10^{-27} \text{ kg}. By using the equation above, we can find the energy equivalent:

First, calculate the energy for 1 amu:

E = (1.66053906660 \times 10^{-27} \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2

The calculation gives:

E = 1.49241808560 \times 10^{-10} \text{ Joules}

This energy is typically expressed in mega-electronvolts (MeV), and the conversion factor from Joules to electronvolts is:

1 \, \text{eV} = 1.60218 \times 10^{-19} \text{ Joules}

Thus, converting from Joules to MeV:

E = \frac{1.49241808560 \times 10^{-10}}{1.60218 \times 10^{-13}} MeV

This gives approximately:

E \approx 931 \text{ MeV}

Hence, the correct answer is 931 MeV, which matches the provided correct option. The conversion and calculation process involves understanding the relationship between mass and energy and using appropriate unit conversions to reach the final result.