Obtain An Expression For The Radius Of Bohr Orbit.

Sure, here is the step by step derivation for the expression of the radius of a Bohr orbit:

1. According to Bohr's model, the centripetal force required for the electron to move in a circular path is provided by the electrostatic force of attraction between the electron and the nucleus. This gives us the equation:

   mv²/r = kZe²/r²

   where: m = mass of the electron v = velocity of the electron r = radius of the orbit k = Coulomb's constant Z = atomic number e = charge of the electron

2. According to the quantization condition of angular momentum given by Bohr, the angular momentum of the electron is an integral multiple of h/2π. This gives us the equation:

   mvr = nh/2π

   where: h = Planck's constant n = principal quantum number (orbit number)

3. From these two equations, we can eliminate v (velocity of the electron) to get an expression for r (radius of the orbit).

   Substituting the value of v from the second equation into the first equation, we get:

   m(nh/2πr)²/r = kZe²/r²

4. Simplifying this equation, we get the expression for the radius of the Bohr orbit:

   r = n²h²/4π²mkZe²

This is the expression for the radius of a Bohr orbit. It shows that the radius of the orbit is directly proportional to the square of the principal quantum number (n²), and inversely proportional to the atomic number (Z).