Calculate the binding energy of an  α- particle. Given that mass of proton = 1.0073 u , mass of neutron = 1.0087 u. and mass of  α – particle = 4.0015 u.

Q: Calculate the binding energy of an  α- particle. Given that mass of proton = 1.0073 u , mass of neutron =
1.0087 u. and mass of  α – particle = 4.0015 u.

Sol: m_p = 1.0073 u , m_n = 1.0087 u , M = 4.0015 u

N = A – Z = 4 – 2 = 2 (∵ ₂He⁴ = _ZX^A )

B.E = Δ m x 931.5 MeV

= {[ Z m_p + (A-Z)m_n ]- M } × 931.5

[(2 ×1.0073)+ (2 × 1.00987)– 4.0015] × 931.5 MeV

= 0.0305 × 931.5 MeV ; B.E = 28.4 MeV.