The Bohr Model and Electron Waves

The Bohr model of the atom, developed by Niels Bohr in 1913, describes electrons as orbiting the nucleus in specific energy levels or shells. These shells are designated by integers (n=1, 2, 3, etc.), with larger values of n corresponding to higher energy levels. The electron in question is in the 3rd orbit, which means it is in the third energy level.

Electron Waves and Revolutions

According to quantum mechanics, electrons can also exhibit wave-like properties. Each electron in an atom can be described by a wave function, which represents the probability of finding the electron at a particular location.

In the context of the Bohr model, the electron can be visualized as a standing wave that wraps around the nucleus in its orbit. The wavelength of this standing wave is related to the electron's energy level and can be calculated using the formula:

λ = 2πr/n

where λ is the wavelength, r is the radius of the orbit, and n is the energy level.

Number of Waves in One Complete Revolution

To find the number of waves made by the electron in one complete revolution in its 3rd orbit, we need to determine the circumference of the orbit and divide it by the wavelength. The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference and r is the radius of the orbit.

Since the radius of the orbit is directly proportional to the energy level (n) in the Bohr model, we can rewrite the formula as:

C = 2πnr

Substituting the value of r from the wavelength formula:

C = 2πn(λ/2π)

The 2π terms cancel out, resulting in:

C = nλ

We can now determine the number of waves in one complete revolution by dividing the circumference by the wavelength:

Number of waves = C/λ = (nλ)/λ = n

Therefore, in the case of the electron in the 3rd orbit, the number of waves made in one complete revolution is 3.