Assuming the radius of a hydrogen atom is given by the Bohr radius, r_Bohr = 5.29 × 10^-¹¹ m, what is the ratio of the nuclear density of a hydrogen atom to its atomic density? Note: Assume for this calculation that the mass of the atom is equal to the mass of the proton. A)1.2 × 10^-¹⁴ B)4.4 × 10⁴ C)8.6 × 10¹³ D)3.9 × 10¹⁷ E)2.3 × 10^-⁵

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Quizplus · Accepted Answer

The nuclear density is given by the ratio of the mass of the nucleus to the volume of the nucleus. The atomic density is given by the ratio of the mass of the atom to the volume of the atom. Since the mass of the atom is equal to the mass of the proton, the ratio of the nuclear density to the atomic density is equal to the ratio of the volume of the atom to the volume of the nucleus. The volume of the atom is given by 4/3πr^3, where r is the radius of the atom. The volume of the nucleus is given by 4/3πr^2, where r is the radius of the nucleus. Therefore, the ratio of the nuclear density to the atomic density is equal to (4/3πr^3)/(4/3πr^2) = r. The radius of the hydrogen atom is given by the Bohr radius, r_Bohr = 5.29 × 10^-¹¹ m. Therefore, the ratio of the nuclear density to the atomic density is equal to r_Bohr = 5.29 × 10^-¹¹ m.

Assuming the Radius of a Hydrogen Atom Is Given by the Bohr