Mass Defect Calculation of Carbon Twelve Atom

To find the mass defect of the ${}_{6}^{12}\text{C}$ atom, we first determine the total mass of its constituent nucleons (protons and neutrons).

The ${}_{6}^{12}\text{C}$ atom consists of:

• Number of protons, $Z = 6$
• Number of neutrons, $N = A - Z = 12 - 6 = 6$

Given:

• Mass of a proton, $m_p = 1.00727\text{ u}$
• Mass of a neutron, $m_n = 1.00866\text{ u}$
• Mass of ${}_{6}^{12}\text{C}$ atom, $M = 12\text{ u}$
• $1\text{ u} = 931.5\text{ MeV}/c^2$

Step 1: Calculate the total mass of individual nucleons

$m_{\text{total}} = Z \cdot m_p + N \cdot m_n$ $m_{\text{total}} = 6 \times 1.00727\text{ u} + 6 \times 1.00866\text{ u}$ $m_{\text{total}} = 6 \times (1.00727 + 1.00866)\text{ u}$ $m_{\text{total}} = 6 \times 2.01593\text{ u} = 12.09558\text{ u}$

Step 2: Calculate the mass defect ($\Delta m$)

The mass defect is the difference between the total mass of individual nucleons and the actual mass of the atom: $\Delta m = m_{\text{total}} - M$ $\Delta m = 12.09558\text{ u} - 12\text{ u} = 0.09558\text{ u}$

Step 3: Convert the mass defect into $\text{MeV}/c^2$

$\Delta m = 0.09558 \times 931.5\text{ MeV}/c^2$ $\Delta m = 89.03277\text{ MeV}/c^2 \approx 89.03\text{ MeV}/c^2$

Thus, the correct option is B.