Take the nuclear radius as R=1.2x10^-15A^1/3 m and the mass of a nucleon as 1.67x10^-27 kg. Find the density of a nucleus of mass number 64 in units of 10^17 kg m^-3, to two decimals.

JEE Main levelNumerical answerDifficulty 2 of 3as027

Take the nuclear radius as $R = 1.2 \times 1 0^{- 15} A^{1/3} m$ and the mass of a nucleon as $1.67 \times 1 0^{- 27} kg$ . Find the density of a nucleus of mass number 64 in units of $1 0^{17} kg m^{- 3}$ , to two decimals.

Numerical answer type, answer in x 10^17 kg/m^3, tolerance 0.03.

R = 1.2e-15 x

6 4^{1/3}

= 4.80e-15 m, so volume = (4/3) pi

R^{3}

= 4.632e-43

m^{3}

. Mass = 64 x 1.67e-27 = 1.069e-25 kg. Density = 2.307e+17

k g / m^{3}

= 2.31 x

1 0^{17}