Question:

The mass of helium atom of mass number $4$ is $4.0026$ amu, while that of the neutron and proton are $1.0087$ and $1.0078$ respectively on the same scale. Hence, the nuclear binding energy per nucleon in the helium atom is nearly

Updated On: Jan 18, 2023
  • 5 MeV
  • 7 MeV
  • 10 MeV
  • 14 MeV
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is B

Solution and Explanation

He atom has $ 2p+2n $
Hence,
$ \Delta m=(2\times 1.0078+2\times 1.0087)-4.0026 $
$ =0.0304\,amu $
$ \therefore $ energy released
$ =0.0304\times 931.5\,MeV $
$ =28.3\,MeV $
Binding energy per nucleon
$ =\frac{28.3}{4}=7\,MeV $ (approximately)
Was this answer helpful?
0
0

Concepts Used:

Nuclear Physics

Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons

Radius of Nucleus

‘R’ represents the radius of the nucleus. R = RoA1/3

Where,

  • Ro is the proportionality constant
  • A is the mass number of the element

Total Number of Protons and Neutrons in a Nucleus

The mass number (A), also known as the nucleon number, is the total number of neutrons and protons in a nucleus.

A = Z + N

Where, N is the neutron number, A is the mass number, Z is the proton number

Mass Defect

Mass defect is the difference between the sum of masses of the nucleons (neutrons + protons) constituting a nucleus and the rest mass of the nucleus and is given as:

Δm = Zmp + (A - Z) mn - M

Where Z = atomic number, A = mass number, mp = mass of 1 proton, mn = mass of 1 neutron and M = mass of nucleus.