Question

: Helium nucleus is composed of two protons and two neutrons. If the atomic mass is \[4.00388\], how much energy is released when the nucleus is constituted?
(Mass of proton = \[1.00757\], Mass of neutron = \[1.00893\])
A. $271MeV$
B. $27.12MeV$
C. $2710MeV$
D. $2.71MeV$

Answer 1

Hint: Proton and neutron constitute the nucleus of an atom they are collectively known as nucleons. The energy required to split or constitute a nucleus of an atom is known as nuclear binding energy. The mass defect of a nucleus is equal to the difference of mass of the nucleon and the mass of the energy binding the nucleus.

Complete step by step answer: If a helium nucleus is to break into protons and neutron energy has to be supplied or added. Alternatively if the helium nucleus is to be constituted from protons and neutrons the energy will be released.
According to the equation, $E = m{c^2}$ , where \[E\] is the energy, \[m\] is the mass and \[c\] is the speed of light, the mass defect can be used to calculate the energy added or released for the breaking or making of a nucleus.
The mass defect is represented as \[\Delta m\]. The actual mass will be less than the sum of the individual masses of the constituent’s proton and neutron because energy is removed when the nucleus is formed. Therefore the mass defect can be calculated as:
$\Delta m = 2 \times {m_p} + 2 \times {m_n} - {m_{He}}$
Where ${m_p}$ = mass of proton,
${m_n}$ =mass of neutron,
${m_{He}}$ = mass of helium nucleus.
Given ${m_p} = 1.00757amu,{m_n} = 1.00893amu,{m_{He}} = 4.00388amu$
$\Delta m = 2 \times 1.00757 + 2 \times 1.00893 - 4.00388$
\[\Delta m = 0.02912amu.\]
We know, \[1amu\] is equivalent to \[931.5MeV\] of energy.
Thus the energy released when the nucleus is constituted can be calculated as:
$E = \Delta m \times 931.5$
$E = 0.02912 \times 931.5MeV$
\[E = 27.12MeV\].
So option B is the correct answer.

Note: The magnitude of binding energy is used to determine whether the nucleus is breaking or forming. It can be positive or negative. The mass defect and binding energy are directly proportional to each other. The higher the mass defect the higher will be the energy required to form the nucleus.