Question

Calculate the binding energy of an alpha particle given its mass to be 4.00151 u.

Answer 1

Data: M = 4.00151 u, m_p = 1.00728 u, m_n = 1.00866 u, 1 u = 931.5 MeV/c²

The binding energy of an alpha particle =

(Zm_p + Nm_n - M)c²

= (2m_p + 2m_n - M)c²

= [(2)(1.00728 u) + 2(1.00866 u) - 4.00151 u]c²

= (2.01456 + 2.01732 - 4.00151)(931.5) MeV

= 28.289655 MeV

= 28.289655 × 10⁶ eV × 1.602 × 10^-10 J

= 4.532002731 × 10^-12 J