Question

An alpha particle (${}^{4}He$)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 particle estimated from these data is the closest to

• A. 27.9 MeV
• B. 22.3 MeV
• C. 35.0 MeV
• D. 20.4 MeV

Answer 1

The correct option is A 27.9 MeV

An alpha particle ${(}_2^{4}He)$ has 2 protons and two neutrons.

Mass defect $\Delta M=2m_p+2m_n-m_{He}$

$\therefore$ $\Delta M=2\left(1.00783\right)+2\left(1.00867\right)-4.00300$ $=0.03000$ amu

Binding energy of alpha particle B.E$=\Delta M{c}^2$

$\therefore$ B.E $=0.03000\times 931.5=27.9$ MeV $(\because 1$ amu $c^2=931.5MeV$ $)$