Example

Question:

Find the energy equivalent of one atomic mass unit, first in Joules and then in MeV. Using this, express the mass defect of \( {}^{16}_8 \text{O} \) in MeV/\( c^2 \).

Solution:

\( 1\,\text{u} = 1.6605 \times 10^{-27}\,\text{kg} \)
To convert to energy units, multiply by \( c^2 \): \[ \text{Energy equivalent} = 1.6605 \times 10^{-27} \times (2.9979 \times 10^8)^2~\text{kg m}^2/\text{s}^2 = 1.4924 \times 10^{-10}~\text{J} \] In eV: \[ = \frac{1.4924 \times 10^{-10}}{1.602 \times 10^{-19}}~\text{eV} = 0.9315 \times 10^9~\text{eV} = 931.5~\text{MeV} \] So, \( 1~\text{u} = 931.5~\text{MeV}/c^2 \)
For \( {}^{16}_8 \text{O} \), \( \Delta M = 0.13691~\text{u} \): \[ 0.13691 \times 931.5~\text{MeV}/c^2 = 127.5~\text{MeV}/c^2 \] The energy needed to separate \( {}^{16}_8 \text{O} \) into its constituents is thus \( 127.5~\text{MeV}/c^2 \).