Hydrogen Atom Structure and Electron Movement

How does a hydrogen atom's structure look like?

A hydrogen atom contains a single electron that moves in a circular orbit about a single proton. Assume the proton is stationary and the electron has a speed of 6.1 x 10^5 m/s.

What is the radius between the stationary proton and the electron orbit within the hydrogen atom?

Answer:

Radius between electron and proton = 6.804 x 10^-10 m

Explanation:

The motion of the electron is carried out in the orbit due to the balancing of the electrostatic force between the proton and the electron and the centripetal force acting on the electron.

The electrostatic force is given by Coulomb's law constant as F = kq1q2/r^2, where k = 9 x 10^9 N-m²/C², q1 and q2 = charges = 1.6 x 10^-19 C, and r = radius between the proton and the electron.

The centripetal force on the moving electron is given by F = meV^2/r, where me = mass of the electron (9.1 x 10^-31 kg) and V = velocity of the moving electron (6.1 x 10^5 m/s).

By equating the electrostatic force and centripetal force formulas, we get r = kq1q2/(meV^2).

Substituting the values into the formula, we find: r = (9 x 10^9) x (1.6 x 10^-19)^2 / (9.1 x 10^-31) x (6.1 x 10^5)^2 = 6.804 x 10^-10 m.