Read the following statements :
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options.
Solution
<p>We know,</p>
<p>Radius of nucleus, $r = {r_0}{A^{{1 \over 3}}}$</p>
<p>where, A = mass number</p>
<p>$\therefore$ Volume $(v) = {4 \over 3}\pi {r^3}$</p>
<p>$= {4 \over 3}\pi r_0^3\,.\,A$</p>
<p>$\therefore$ $v \propto A$</p>
<p>$\therefore$ Volume is directly proportional to mass number.</p>
<p>We know,</p>
<p>density $(d) = {m \over v}$</p>
<p>$= {{z{m_p} + (A - z){m_N}} \over {{4 \over 3}\pi r_0^3{{({A^{1/3}})}^3}}}$</p>
<p>$= {{z{m_p} + A{m_p} - z{m_p}} \over {{4 \over 3}\pi r_0^3A}}$ [$\because$ ${m_p} \simeq {m_N}$]</p>
<p>$= {{A{m_p}} \over {{4 \over 3}\pi r_0^3A}}$</p>
<p>$= {{{m_p}} \over {{4 \over 3}\pi r_0^3}}$</p>
<p>$\therefore$ Density of nucleus is independent of mass number.</p>
About this question
Subject: Physics · Chapter: Atoms and Nuclei · Topic: Nuclear Binding Energy
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