2003 AIPMT NucleiMass defect and binding energy Easy Question 5 of 5 in Mass defect and binding energy

The mass of proton is 1.0073 u and that of neutron is 1.0087 u (u = atomic mass unit). The binding energy of $^{4}_{2}He$ is (Given : helium nucleus mass $\approx$ 4.0015 u)

A 0.0305 J
B 0.0305 erg
C 28.4 MeV
D 0.061 u

The answer is C.

Solution

$^{4}_{2}He$ has 2 protons and 2 neutrons.
Mass defect: $\Delta m = [2(1.0073) + 2(1.0087)] - 4.0015 = 4.0320 - 4.0015 = 0.0305$ u
Binding energy: $BE = \Delta m \times 931$ MeV
$= [2(1.0087 + 1.0073) - 4.0015] \times 931 = 0.0305 \times 931$
$BE \approx 28.4$ MeV
(In joules this is about $4.5 \times 10^{-12}$ J, not 0.0305 J or erg; and 0.0305 u is the mass defect, not 0.061 u.)

Concept Binding energy of helium nucleus

Mass defect and binding energy in past papers

5 questions from this chapter have appeared across 5 exam years.