question_answer

Define mass number (A) of an atomic nucleus. Assuming the nucleus to be spherical, give the relation between mass number (A) and the radius (R) of the nucleus.                                   Calculate the density of nuclear matter. Radius of nucleus of \[_{1}^{1}H=1.1\times {{10}^{-15}}\overset{\text{o}}{\mathop{\text{A}}}\,\] . What is the ratio of the order of magnitude of density of nuclear matter and density of ordinary matter?       

Answer:

                The total number of protons and neutrons present inside a nucleus is called its mass number (A). The relation between the mass number (A) and radius (R) of the nucleus is \[R={{R}_{0}}{{A}^{1/3}},\] where \[{{R}_{0}}=1.1\times {{10}^{-15}}m\] Density of nuclear matter \[\rho =\frac{\text{Mass of}_{\text{1}}^{\text{1}}\text{ H}}{\text{Volume}}=\frac{1.66\times {{10}^{-27}}kg}{\frac{4}{3}\pi {{(1.1\times {{10}^{-15}}m)}^{3}}}\] \[=3\times {{10}^{17}}kg{{m}^{-3}}\] \[\frac{\text{Density of nuclear matter}}{\text{Density of ordinary matter}}=\frac{{{10}^{17}}}{{{10}^{3}}}=\mathbf{1}{{\mathbf{0}}^{\mathbf{14}}}\]