An alpha particle (24He) has a mass of 4.00300 amu. A proton has mass of 1.00783 amu and a neutron has mass of 1.00867 amu respectively. The binding energy of alpha particles estimated from these data is the closest to.(1) 20.4 MeV(2) 32.0 MeV(3) 24.3 MeV(4) 27.9 MeV

Answer: (4) 27.9 MeV

Consider an alpha particle (24He),

Number of p[rotons = 2

Number of Neutrons = 2

The mass defect formula 

ΔM = 2mp + 2mn – mHe

ΔM = 2 ✕ (1.00783) + 2 ✕ (1.00867) – 4.00300

ΔM = 2.0157 + 2.0173 – 4.00300

∴ ΔM = 0.03 amu

Formula to calculate bonding energy of the alpha particle

B.E = ΔMc2

1 amu c2 = 931.5MeV

B.E = 0.03 ✕ 931.5

B.E = 27.9 MeV

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