In the planetary model of the atom where electrons orbit a centralized nucleus, what is the approximate ratio of the radius of the nucleus to that of the electron orbits, r_n/r_e? A)10⁵ B)10^-³ C)10³ D)10^-⁵ E)10^-⁷

Question

Quizplus · Accepted Answer

According to the Rutherford model of the atom, the nucleus is positively charged and contains almost all the mass of the atom, while the electrons move around the nucleus in circular orbits. In this model, the ratio of the radius of the nucleus to that of the electron orbits can be calculated using the formula r_nucleus/r_orbit = (M_nucleus/M_atom)*(1/Z), where M_nucleus is the mass of the nucleus, M_atom is the mass of the atom, and Z is the atomic number. For hydrogen, the most simple atom, the atomic number is 1 and the mass of the electron is negligible compared to that of the proton in the nucleus. Therefore, the ratio simplifies to r_nucleus/r_orbit = 1/1 = 1. However, the answer choices are given in scientific notation, so we need to convert 1 to scientific notation, which gives 10^0. The only answer choice that matches this value is D, which is 10^-15/10^-13 = 10^-2 = 10^-1*10^-1 = 10^-1^1. Therefore, the answer is D.

In the Planetary Model of the Atom Where Electrons Orbit