Solved Examples of Structure of Nucleus
Example 1: Compare the radii of two nuclei with mass numbers 1 and 27 respectively.
Solution:
Radius of nucleus R = R0A1/3
[Tex]\frac{R_1}{R_2}= \big(\frac{A_1}{A_2}\big)^{1/3} [/Tex]
R1/R2 = (1/27)1/3
= 1/3
Example 2: What is the nuclear radius of 125Fe if that of 27Al is 3.6 fermi?
Solution:
Nuclear radius, R = R0A1/3 ⇒ R∝A1/3
For Al, A = 27, RAl = 3.6 fermi,
For Fe A = 125
[Tex]\frac{R_{Fe}}{R_{Al}}= \big(\frac{A_{Fe}}{A_{Al}}\big)^{1/3} [/Tex]
RFe/RAl = (125/27)1/3
RFe = (5/3)RAl
= (5/3) ×3.6 fermi
RFe = 6 fermi
Example 3: A neutron breaks into a proton and electron. Calculate the energy produced in this reaction in MeV. Mass of an electron = 9.1 ×10-31 kg, Mass of proton = 1.6725×10-27 kg, Mass of neutron 1.6747×10-27 kg. Speed of light = 3×108 ms-1.
Solution:
Mass defect (△)m = Mass of neutron – (mass of proton + mass of electron)
△m = [(1.6747×10-27) – (1.6725×10-27 + 9.1 ×10-31)]
△m = 0.0013×10-27 kg
Energy released Q = △mc2
Q = (0.0013×10-27) × (3×108)2
= 1.17×10-13 J
Q = (1.173×10-13) / (1.6×10-19)
= 0.73×106 eV
Q = 0.73 MeV
Example 4: Find the binding energy of 126C. Also, find the binding energy per nucleon. Given mass of 11H = 1.0078 u, 10n =1.0087 u, 126C = 12.00004u.
Solution:
One atom of 126C consists of 6 protons, 6 electrons, and 6 neutrons. The mass of the uncombined protons and electrons is the same as that of six 11H atoms.
Mass of six 11H atoms = 6×1.0078 = 6.0468 u
Mass of six neutrons = 6 × 1.0087 = 6.0522 u
Total mass of particles = 6.0468 +6.0522
= 12.0990 uMass of 126C atom = 12.00004
Mass defect = 12.0990 – 12.00004
= 0.0990Binding energy = 931 × (0.099)
= 92 MeVBinding energy per nucleon = 92/12
= 7.66 MeV
Structure of Nucleus
The nucleus of an atom consists of two types of particles, positively charged particles called protons and neutrally charged particles called neutrons. Protons + Neutrons in an atom represent the nucleus of an atom. The nucleus of an atom is represented by ZXA, where X is the nucleus of an atom, Z is the atomic number and A is the mass number.
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