Question

The carbon isotope \( {}^{12}_6C \) has a nuclear mass of 12.000000 u. Calculate the binding energy of its nucleus.

Hint:

The binding energy is a measure of the energy required to disassemble the nucleus into its constituent protons and neutrons.

Answer 1

The binding energy of a nucleus is given by the formula: \[ B.E. = \left( Zm_p + (A - Z)m_n - M_N \right) \times 931.5 \, \text{MeV}, \] where: - \( Z \) is the atomic number, - \( A \) is the mass number, - \( m_p \) is the mass of a proton, - \( m_n \) is the mass of a neutron, - \( M_N \) is the nuclear mass. For \( {}^{12}_6C \), \( Z = 6 \), \( A = 12 \), and the given masses are: \[ m_p = 1.007825 \, \text{u}, \, m_n = 1.008665 \, \text{u}, \, M_N = 12.000000 \, \text{u}. \] Thus, the binding energy is: \[ B.E. = \left( 6 \times 1.007825 + 6 \times 1.008665 - 12.000000 \right) \times 931.5 \, \text{MeV}. \] After calculation: \[ B.E. = 92.16 \, \text{MeV}. \]