Suppose that the mass of a nucleus is roughly given by M = A m_p , where A represents the mass number. Estimate the density of matter inside a nucleus in kg m ⁻³ , and determine the specific gravity of nuclear matter.

Step-by-step solution

The mass of the nucleus is given by M = A m_p , where A is the mass number and m_p 1.67 10⁻²⁷ kg . The radius of the nucleus is R = R₀ A^ 1/3 , where R₀ 1.1 10⁻¹⁵ m . The volume of the nucleus is: V = 4 3 R^3 = 4 3 R₀^3 A The density of nuclear matter is: = M V = A m_p 4 3 R₀^3 A = m_p 4 3 R₀^3 Substituting the standard values: = 1.67 10⁻²⁷ 4 3 (1.1 10⁻¹⁵)^3 3 10¹⁷ kg m ⁻³ The specific gravity is the ratio of the density of the nuclear matter to the density of water ( _w = 10^3 kg m ⁻³ ): Specific gravity = _w = 3