An unknown nucleus has a nuclear density of 2.29 10¹⁷ kg/m ^3 and mass of 19.926 10⁻²⁷ kg. Its mass number A is approximately : (Take R₀ = 1.2 10⁻¹⁵ m; 4 = 12.56 )

Step-by-step solution

The nuclear density is given by the ratio of the mass of the nucleus to its volume: = m 4 3 R^3 The radius of the nucleus is R = R₀ A^ 1/3 , which gives R^3 = R₀^3 A . Substituting this into the density formula: = 3m 4 R₀^3 A Rearranging for the mass number A : A = 3m 4 R₀^3 Substituting the given values: A = 3 19.926 10⁻²⁷ 12.56 (1.2 10⁻¹⁵)^3 2.29 10¹⁷ A = 59.778 10⁻²⁷ 12.56 1.728 10⁻⁴⁵ 2.29 10¹⁷ A = 59.778 10⁻²⁷ 49.7 10⁻²⁸ A = 597.78 49.7 12 Answer: 12