The masses of neutron and proton are 1.0087 and 1.0073 amu respectively- If the neutrons and protons combine to form helium nucleus of mass 4.0015 amu the binding energy of the helium nucleus will be

Question

The masses of neutron and proton are 1.0087 and 1.0073 amu respectively- If the neutrons and protons combine to form helium nucleus of mass 4.0015 amu the binding energy of the helium nucleus will be (A) 28.4 MeV (B) 20.8 MeV (C) 27.3 MeV (D) 14.2 MeV

Tardigrade Admin · Accepted Answer

Mass defect, Δ hatm=2(mn+mp)-m He (∵ helium nucleus has two protons and two neutrons) ∴ Δ m =2(1.0087+1.0073)-4.0015 =4.032-4.0015=0.0305 Binding energy, EB =Δ m × 931 MeV =0.0305 × 931 =28.4 MeV

Q. The masses of neutron and proton are $1.0087$ and $1.0073$ amu respectively- If the neutrons and protons combine to form helium nucleus of mass $4.0015$ amu the binding energy of the helium nucleus will be

28.4 MeV

20.8 MeV

27.3 MeV

14.2 MeV

Mass defect, $Δ \overset{m}{^} = 2 (m_{n} + m_{p}) - m_{He}$
$(∵$ helium nucleus has two protons and two neutrons)
$∴ Δ m = 2 (1.0087 + 1.0073) - 4.0015$
$= 4.032 - 4.0015 = 0.0305$
Binding energy,
$E_{B} = Δ m \times 931 M e V$
$= 0.0305 \times 931$
$= 28.4 M e V$

Q. The masses of neutron and proton are 1.0087 and 1.0073 amu respectively- If the neutrons and protons combine to form helium nucleus of mass 4.0015 amu the binding energy of the helium nucleus will be