Take the radius of an aluminium-27 nucleus as R=1.2x10^-15A^1/3 m and the radius of the atom as 1.5x10^-10 m. The fraction of the atomic volume occupied by the nucleus is xx10^-14. Find x to two decimals.

JEE Advanced levelNumerical answerDifficulty 3 of 3as045

Take the radius of an aluminium-27 nucleus as $R = 1.2 \times 1 0^{- 15} A^{1/3} m$ and the radius of the atom as $1.5 \times 1 0^{- 10} m$ . The fraction of the atomic volume occupied by the nucleus is $x \times 1 0^{- 14}$ . Find $x$ to two decimals.

Numerical answer type, tolerance 0.05.

R = 1.2e-15 x

2 7^{1/3}

= 1.2e-15 x 3 = 3.60e-15 m. Volume ratio =

(R / r_{a t o m})^{3}

(3.60 e - 15/1.5 e - 10)^{3}

= 1.382e-14, so x = 1.38.