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