Calculate the mass defect and the binding energy of the alpha particle $^{4}_{2}\text{He}$, given: mass of hydrogen atom $m_H = 1.007825\ \text{u}$, mass of neutron $m_n = 1.008665\ \text{u}$, mass of $^{4}_{2}\text{He}$ atom $M = 4.002603\ \text{u}$.

Calculate the mass defect and the binding energy of the alpha particle ⁴₂He, given: mass of hydrogen atom mH =

Example · Example 9

^{4}_{2}\text{He}

West Bengal WbchseTextbookSubjectiveImportance★★★★★est

28% · 9/32 Questions

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

For $^4_2\text{He}$ , $Z=2$ protons and $A-Z=2$ neutrons. The mass defect is

\Delta m = [2m_H + 2m_n] - M = [2(1.007825) + 2(1.008665)] - 4.002603

= [2.015650 + 2.017330] - 4.002603 = 4.032980 - 4.002603 = 0.030377\ \text{u}

Converting to energy using $1\ \text{u}=931.5\ \text{MeV}$ :

$BE = 0.030377\times931.5 \approx 28.3\ \text{MeV}$ …