## Nuclei

# 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 = R
_{0}A^{1/3}(R_{0}= 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 × 10
^{17}kg/m^{3} - 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

### View the Topic in this video From 00:04 To 16:27

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

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/m^{3}