Atomic Masses and Composition of Nucleus, Size of the Nucleus

• Rutherford’s α-ray scattering experiment lead to the discovery of nucleus.
• MASS NUMBER is given as the total number of protons and neutrons inside the nucleus. A = Z + N
• The nuclei having the same atomic number, Z but different mass numbers, A are called ISOTOPES. Ex : \tt ^{1}_{1}H, ^{2}_{1}H, ^{3}_{1}H are isotopes of oxygen.
• The nuclei having the same neutron number, N but different atomic numbers Z are called ISOTONES: Ex: \tt ^{198}_{80}Hg, ^{197}_{79}Au
• Nuclei having the same atomic number, Z and mass number, A but with different nuclear properties such as radioactive decay and magnetic moments are called ISOMERS.
• The nuclei having the same mass number, A but different atomic numbers, Z are called ISOBARS: Ex: \tt ^{14}_{6}C, ^{14}_{7}N
• If an α-particle with K.E, E approaches the target with atomic number Z, if the closest distance is "d" then \tt E = \frac{1}{4 \pi \varepsilon_{0}} \frac{2 ze^{2}}{d}
• The nucleus with radius R and mass number A is given by R = R0 A1/3 (R0 = 1.2 × 10−15 m = 1.2 fermi)
• NUCLEAR DENSITY = \tt \frac{MASS}{VOLUME}= \frac{A \times 1.66 \times 10^{-27}}{\frac{4}{3} \pi R_{0}^{3} A}
• Density of the nucleus = 2.3 × 1017 kg/m3
• Density of the nucleus is independent of mass number (d ∝ A)
• Density of nuclei of all atoms is same.
• Atomic Mass Unit, 1 amu = 1.660565 × 10−27 kg

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1. Nuclear volume : The volume of nucleus is given by V = \frac{4}{3}\pi R^{3} = \frac{4}{3}\pi \ R^{3}_{0} \ A ⇒ V ∝ A

2. Mass per unit volume of a nucleus is called nuclear density.
Nuclear denisty (ρ) = \tt \frac{Mass \ of \ nucleus}{Volume \ of \ nucleus} = \frac{mA}{\frac{4}{3} \pi (R_{0}A^{1/3})^{3}}

3. Number of nucleon per unit volume
\tt \frac{Density \ of \ Nucleus}{Mass \ of \ One \ Nucleon} = \frac{10^{17}}{1.67 \times 10^{-27}} \cong 10^{44} Nucleon/m3