**Number of Waves made by a Bohr Electron in One Complete Revolution in its Fourth Orbit**

In the Bohr model of the atom, electrons are considered to move in specific orbits or energy levels around the nucleus. These orbits are quantized, meaning that the electron can only exist in certain discrete energy levels. Each orbit is characterized by a principal quantum number, denoted by n, where n = 1, 2, 3, and so on.

The number of waves made by a Bohr electron in one complete revolution can be determined by analyzing the circumference of its orbit and the wavelength of the electron.

**Formula for Circumference:**

The circumference of an orbit can be determined using the formula:

C = 2πr

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

**Formula for Wavelength:**

The wavelength of an electron can be calculated using the de Broglie equation:

λ = h / (mv)

Where λ is the wavelength, h is the Planck's constant (6.626 x 10^-34 J·s), m is the mass of the electron, and v is the velocity of the electron.

**Relationship between Wavelength and Circumference:**

The circumference of an orbit can be related to the wavelength of the electron by the following equation:

C = nλ

Where n is the number of waves made by the electron in one complete revolution.

**Calculating the Number of Waves:**

To determine the number of waves made by a Bohr electron in its fourth orbit, we need to find the circumference and wavelength of the orbit.

1. Radius of the Fourth Orbit:
- According to the Bohr model, the radius of the nth orbit is given by the equation:
r = (0.529 × n^2) / Z

- For the fourth orbit, n = 4 and Z is the atomic number of the atom.

2. Circumference of the Fourth Orbit:
- Using the formula C = 2πr, we can calculate the circumference of the fourth orbit.

3. Wavelength of the Electron:
- Using the de Broglie equation, we can calculate the wavelength of the electron in the fourth orbit.

4. Determining the Number of Waves:
- By substituting the values of C and λ into the equation C = nλ, we can solve for n, which represents the number of waves made by the electron in one complete revolution in its fourth orbit.

By following these steps, you can calculate the number of waves made by a Bohr electron in its fourth orbit. Remember to use the appropriate formulas and values to obtain an accurate result.

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