The mass of proton, neutron and helium nucleus are respectively 1… — Solution | JEE Physics

MCQEasyJEE 2023Atomic Mass & Binding Energy

The mass of proton, neutron and helium nucleus are respectively $1.0073$ u, $1.0087$ u and $4.0015$ u. The binding energy of helium nucleus is:

A
$14.2$ MeV
B
$28.4$ MeV
C
$56.8$ MeV
D
$7.1$ MeV

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Mass of proton $= 1.0073 \, \text{u}$ , mass of neutron $= 1.0087 \, \text{u}$ , mass of helium nucleus $= 4.0015 \, \text{u}$ .

Find: Binding energy of the helium nucleus.

Use the mass defect relation:

B.E. = (2m_p + 2m_n - m_{\text{He}})c^2

Substituting the given values:

B.E. = (2m_p + 2m_n - m_{\text{He}})c^2 = 28.4 \, \text{MeV}

Therefore, the binding energy of helium nucleus is $28.4 \, \text{MeV}$ . The correct option is B.

The solution also shows one header stating option D, but its working concludes $28.4 \, \text{MeV}$ ; hence the worked value is taken as authoritative.

Common mistakes

Using the mass of helium atom instead of the helium nucleus is incorrect because electron masses would then be included. Use the nuclear mass exactly as given in the question.
Forgetting that helium has 2 protons and 2 neutrons gives a wrong mass defect. Write the nucleus composition first, then substitute in $2m_p + 2m_n - m_{\text{He}}$ .
Subtracting in the wrong order, such as $m_{\text{He}} - (2m_p + 2m_n)$ , gives a negative value. Binding energy comes from a positive mass defect of separated nucleons minus nucleus mass.

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Answer

Step-by-step solution

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