Read the following passage and answer the questions.
A nucleus is written as \({}^{A}_{Z}\mathrm{X}\), where X is the chemical symbol of the element. Here Z is the atomic number and A is the mass number. The nucleus contains Z protons and (A − Z) neutrons. Protons and neutrons are together called nucleons. For example, the aluminium nucleus \({}^{27}_{13}\mathrm{Al}\) has 13 protons and 14 neutrons. Experiments show that a nucleus of mass number A has a radius \(R=R_0A^{1/3}\), where \(R_0=1.2\ \mathrm{fm}\) and 1 fm = \(10^{-15}\ \mathrm{m}\). The protons in a nucleus are positively charged, so they repel each other. Still, the nucleus does not fly apart. The nucleons are held together by a force of a different kind, called the nuclear force. A rough graph of the potential energy of a pair of nucleons against their separation r has a minimum at a separation \(r_0\) of about 0.8 fm.
The radius of the \({}^{27}_{13}\mathrm{Al}\) nucleus is about
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3.6 fm
The radius of a nucleus grows as the cube root of its mass number. For aluminium, \( A=27 \), and the cube root of 27 is 3.
Given:
\( R_0=1.2\ \mathrm{fm} \)
\( A=27 \)
\( \begin{aligned} R &= R_0A^{1/3} \\ &= 1.2\times(27)^{1/3} \\ &= 1.2\times3 \\ &= 3.6\ \mathrm{fm} \end{aligned} \)
Therefore, the radius of the \( {}^{27}_{13}\mathrm{Al} \) nucleus is about 3.6 fm.
NCERT (2026-27):
Size of the Nucleus – “It has been found that a nucleus of mass number A has a radius R = R0 A1/3 … where R0 = 1.2 × 10–15 m (=1.2 fm; 1 fm = 10–15 m).”