24.141 CP - Chemistry: Molecular Nature Of Matter And Change

Question

Use Einstein’s equation, the mass in grams of 1  amu, and the relation between electron volts and joules to find the energy equivalent (in MeV) of a mass difference of 1  amu.

Step-by-Step Solution

Answer

The energy equivalent (in MeV) of a mass difference of 1 amu is 931.5 MeV.

Step 1: Nuclear energy

Nuclear energy is generated by protons and neutrons in the nucleus, the atom's centre. This type of energy can be generated in two ways: fission, which occurs when atom nuclei split into several pieces, or fusion, which occurs when nuclei fuse together.

Step 2: Calculation

From Einstein's equation:

 $E=m{c}^2$

  $$\begin{gathered} E=\frac{1 amu\times 1.66\times {10}^{-24} g/amu\times {\left(3.0\times {10}^8 cm/s\right)}^2}{1.602\times {10}^{-19}\times {10}^6 C} \\ =931.5 MeV \end{gathered}$$