Bohr's Theory of Hydrogen Atom
In Bohr's theory of the hydrogen atom, the speed of the electron in a stable orbit is related to the principal quantum number (n) through a constant value (c). This relationship can be explained in detail as follows:

Speed of Electron in Orbit
- In Bohr's model, electrons orbit the nucleus in circular paths at specific distances known as energy levels or orbits.
- The speed of the electron in a stable orbit is determined by the balance between the centripetal force required to keep the electron in its orbit and the electrostatic force of attraction between the electron and the nucleus.

Relationship with Principal Quantum Number (n)
- The principal quantum number (n) in an atom specifies the energy level of the electron and the size of the orbit.
- According to Bohr, the speed of the electron in a stable orbit is inversely proportional to the principal quantum number (n). This means that as n increases, the speed of the electron decreases.
- The relationship can be mathematically expressed as vn = c/n, where c is a constant value.

Implications of the Relationship
- This relationship implies that electrons in higher energy levels have lower speeds compared to electrons in lower energy levels.
- It also suggests that electrons closer to the nucleus (lower energy levels) move at higher speeds than electrons in outer orbits.
- Understanding the speed of electrons in stable orbits is crucial for explaining the stability and behavior of atoms in the context of quantum mechanics.

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