In the Rutherford model of the hydrogen atom, a proton (mass M, charge Q)is the nucleus and an electron (mass m, charge q)moves around the proton in a circle of radius r.Let k denote the Coulomb force constant (1/4$\pi$)and G the universal gravitational constant.The ratio of the electrostatic force to the gravitational force between electron and proton is:

Question

Quizplus · Accepted Answer

The electrostatic force between the electron and proton is given by the Coulomb's law, which states that the force is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The gravitational force between them is given by Newton's law of gravitation, which states that the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Therefore, the ratio of the electrostatic force to the gravitational force between the electron and proton is given by:

kQq/(GMm^2*r^2)

Since we are dealing with the hydrogen atom, we can assume that the mass of the proton is much greater than the mass of the electron (i.e., M >> m). Therefore, we can neglect the mass of the electron in the denominator, and the expression simplifies to:

kQq/(GMmr^2)

which is equivalent to the choice E: kQq/GMm.

In the Rutherford Model of the Hydrogen Atom, a Proton π\piπ

In the Rutherford Model of the Hydrogen Atom, a Proton $\pi$