Size of Nucleus: Class 12 Physics Notes, Definition, Working Principle, Formula & Real-Life Applications

(a) Discovered by: Rutherford

(b) Constituents: include neutrons ( n ) and protons ( p ) [collectively known as nucleons]

1. Neutron : It is a neutral particle. It was discovered by J. Chadwick (in 1932). Mass of neutron, ${\mathrm{m}}_{\mathrm{n}}=1.6749286\times {10}^{-27}\mathrm{k}\mathrm{g}$ .

2. Proton :This has a charge equal to +e . It was discovered by Goldstein.

Mass of proton, ${\mathrm{m}}_{\mathrm{p}}=1.6726231\times {10}^{-27}\mathrm{k}\mathrm{g}$

$m_p\sim m_n$

(c) Representation:

$\begin{array}{ll}\text{zXA}& \text{or}\mathrm{}{}_z^{A}X\\ \text{where}X& \Rightarrow \text{symbol of the atom}\\ Z& \Rightarrow \text{Atomic number = number of protons}\\ & \Rightarrow \text{Atomic mass number = total number of nucleons.}\\ & =\text{no. of protons + no. of neutrons.}\end{array}$

As per NCERT, the definition of Nucleus is as follows:

“According to this the entire positive charge and most of the mass of the atom is concentrated in a small volume called the nucleus with electrons revolving around the nucleus just as planets revolve around the sun.”

Atomic mass number

It is the closest and nearest integer value of mass represented in a.m.u. (atomic mass unit). 1 a.m.u. $=\frac{1}{12}$  [mass of one atom of ${}_6{\mathrm{C}}^{12}$  atom at rest and in ground state]
$1.6603\times {10}^{-27}\mathrm{k}\mathrm{g};931.478\mathrm{M}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$ mass of proton $\left(m_p\right)=$ mass of neutron $\left(m_n\right)=1$ a.m.u.
Some important definitions related to atomic mass number:

(a) Isotopes: The nuclei with same number of protons but with different number of neutrons are known as isotopes.

 

(b) Isotones: Nuclei with the same number of neutron $N$ but different atomic number $Z$  are known as isotones.

 

(c) Isobars : The nuclei with same mass number but has different atomic number are called isobars.

(d) Size of nucleus: Order of ${10}^{-15}\mathrm{m}$ (fermi)

Radius of nucleus; $R=R_0{A}^{1/3}$

where $R_0=1.1\times {10}^{-15}\mathrm{m}$ (which is an empirical constant)

$\mathrm{A}=$ Atomic mass number of atom.

(e) Density : density $=\frac{\text{mass}}{\text{volume}}\cong \frac{A{m}_p}{\frac{4}{3}\pi R^3}=\frac{A{m}_p}{\frac{4}{3}\pi {\left(R_0{A}^{1/3}\right)}^3}=\frac{3m_p}{4\pi R_0{}^3}$

$=\frac{3\times 1.67\times {10}^{-27}}{4\times 3.14\times {\left(1.1\times {10}^{-15}\right)}^3}=3\times {10}^{17}\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$

Nuclei of all atoms have almost same density as nuclear density is independent of mass number ( A ) and atomic number ( Z ).

MASS DEFECT

It has been observed that there is a difference between expected mass and actual mass of a nucleus.

$\begin{array}{rr}& M_{\text{expected}}=Z{m}_p+(A-Z)m_n\\ & M_{\text{observed}}=M_{\text{atom}}-Z{m}_e\end{array}$

It is found that $M_{\text{observed}}<M_{\text{expected}}$
Hence, mass defect is defined as Mass defect $=M_{\text{expected}}-M_{\text{observed}}$

$\mathrm{\Delta }m=\left[Z{m}_p+(A-Z)m_n\right]-\left[M_{\text{atom}}-Z{m}_e\right]$

 

The following steps explain the working principle of nucleus:

• The nucleus acts as the cell's control center, managing all cellular functions and processes
• A nucleus contains DNA (chromosomes) that holds all the genetic instructions for the cell
• It decides which genes are turned on or off at different times.
• Nucleus produces ribosomes in a special area called the nucleolus, which are needed to make proteins
• A double membrane with pores controls what enters and exits the nucleus.
• Nucleus sends RNA instructions from the nucleus to the cytoplasm to make proteins
• Nucleus organises chromosomes during cell division to ensure each new cell gets the right genetic material
• Nucleus receives chemical messages from inside and outside the cell to adjust its activities