Energy Equivalent of 1 Atomic Mass Unit (u)

The question asks about the approximate energy equivalent of 1 atomic mass unit (u). This concept is central to understanding mass-energy conversion, particularly in nuclear physics. The relationship between mass and energy is given by Einstein's famous equation.

Understanding Atomic Mass Unit (u)

The atomic mass unit (u), also known as the unified atomic mass unit, is a standard unit used for indicating mass on atomic and molecular scales. It is defined based on the carbon-12 atom.

• One atomic mass unit (1 u) is defined as exactly one-twelfth (<span class="math">\(\frac{1}{12}\)</span>) of the mass of a carbon-12 atom.
• The approximate value of 1 u in kilograms is \(1.660539 \times 10^{-27}\) kg.

Einstein's Mass-Energy Equivalence

According to Albert Einstein's special theory of relativity, mass and energy are interconvertible. This principle is expressed by the equation:

\(E = mc^2\)

Where:

• \(E\) represents energy.
• \(m\) represents mass.
• \(c\) represents the speed of light in a vacuum.

The speed of light \(c\) is a constant, approximately \(2.99792458 \times 10^8\) meters per second. The \(c^2\) term is very large, which explains why a small amount of mass can be equivalent to a very large amount of energy.

Calculating Energy Equivalent of 1 u in MeV

To find the energy equivalent of 1 u, we use the mass of 1 u and the speed of light in the formula \(E = mc^2\).

Using the approximate value for the mass of 1 u:

\(m \approx 1.660539 \times 10^{-27} \text{ kg}\)

\(c \approx 2.99792458 \times 10^8 \text{ m/s}\)

Substitute these values into the equation:

\(E = (1.660539 \times 10^{-27} \text{ kg}) \times (2.99792458 \times 10^8 \text{ m/s})^2\)

\(E \approx (1.660539 \times 10^{-27}) \times (8.98755 \times 10^{16}) \text{ J}\)

\(E \approx 1.492418 \times 10^{-10} \text{ J}\)

This energy is calculated in Joules. In physics, especially nuclear and particle physics, energy is frequently expressed in mega-electron volts (MeV). We need to convert Joules to MeV.

The conversion factor is:

\(1 \text{ MeV} = 1.602176634 \times 10^{-13} \text{ J}\)

To convert the energy from Joules to MeV, divide the energy in Joules by the conversion factor:

\(E (\text{in MeV}) = \frac{1.492418 \times 10^{-10} \text{ J}}{1.602176634 \times 10^{-13} \text{ J/MeV}}\)

\(E (\text{in MeV}) \approx 931.49 \text{ MeV}\)

This result shows that 1 atomic mass unit is equivalent to approximately 931.49 MeV of energy.

Conclusion on Energy Equivalent

Comparing our calculated value (\(\approx 931.49\) MeV) with the provided options, we find that 931 MeV is the closest value.

Therefore, 1 atomic mass unit (u) is equivalent to about 931 MeV of energy. This value is a standard conversion used in nuclear physics calculations.

Revision Table: Key Constants and Conversions

Additional Information: Significance in Nuclear Physics

The energy equivalent of the atomic mass unit is a fundamental value in nuclear physics calculations because:

• It simplifies the calculation of energy released in nuclear reactions (fission and fusion), where mass is converted into energy.
• Particle masses are often expressed in energy units (like MeV/\(c^2\)), making calculations involving energy and mass transfers more straightforward.

Understanding this conversion allows physicists to directly relate the mass difference in a nuclear reaction to the energy produced or consumed.