A particular heavy nucleus has a total mass of 1.256 10⁻²⁵ kg and a nuclear density of 2.4 10¹⁷ kg/m ^3 . What is the approximate radius of this nucleus? (Take = 3.14 )

Step-by-step solution

The volume of the nucleus is given by V = M Assuming the nucleus to be spherical, V = 4 3 R^3 4 3 R^3 = M R^3 = 3M 4 Substituting the given values: R^3 = 3 1.256 10⁻²⁵ 4 3.14 2.4 10¹⁷ R^3 = 3 1.256 10⁻²⁵ 12.56 2.4 10¹⁷ R^3 = 3 10⁻¹ 10⁻²⁵ 2.4 10¹⁷ R^3 = 3 2.4 10⁻⁴³ R^3 = 1.25 10⁻⁴³ = 125 10⁻⁴⁵ R = (125 10⁻⁴⁵)^ 1/3 = 5.0 10⁻¹⁵ m Answer: 5.0 10⁻¹⁵ m