Chapter : 13

What are Nuclei ?

Topic Name

Radius Nucleus


R = R0A1/3
  • Most of the space in atom is empty.
  • N(θ) ∝(1/sin4(θ/2))
where N(θ) = number of α particles

θ = scattered angle

Symbol Representation

R0 = an empirical constant = 1.1 × 10–15 m

A = mass number of atom

Important Points

  • Nuclear radius is measured in
1 fermi = 10–15 m

Nuclear Density

p= (M/V) 

M = mass of nucleus

V = volume of nucleus

  • Density of nuclear matter is of
    the order of 1017 kg/m3
  • Density of nuclear matter is
    independent of the mass number.

Mass Defect

∆m = [Zmp + (A – Z)mn – M]

Z = atomic number

mp = mass of proton

A = atomic mass

mn = mass of neutron

M = mass of nucleus

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Binding Energy

∆Eb = ∆mc2


∆Eb = ∆m × 931.5 MeV
∆m = mass defect
  • Binding energy is the minimum
    energy required to break the
    nucleus into its constituent

Some Important Concepts


Composition of Nucleus

Definition / Explanation

  • The atomic nucleus consists of two types of elementary particles i.e., protons and neutrons, protons and neutrons are collectively known as nucleons.
  • Atomic number = Number of protons (Z)
  • Mass number (A) = Number of protons (Z) + Number of neutrons (N)
  • Nuclear mass is the total mass of the protons and neutrons measured in amu, 1 atomic mass unit (u) = 931.5 MeV/c2

Nuclear Fission

  • Fusing two or more lighter nuclei to a single heavy nucleus is known as nuclear fusion.
  • Fusion reactions take place in stars and Hydrogen bomb.