Question

Derive expression for radii of bohrs orbit

Answer 1

Answer:

The Bohr Model. where m is the mass of the electron, r is the radius of the orbit, and v is the orbital speed of the electron. 5.29 x 10-11 m is known as the Bohr radius. So, Bohr's assumption that the angular momentum is quantized produces the result that the radii of the electron's allowed orbits are also quantized.

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Answer 2

Answer:

To explain line spectra, Neils Bohr proposed that the angular momentum of the electrons orbiting the atom is quantized:

mvr = nh/2p

where m is the mass of the electron, r is the radius of the orbit, and v is the orbital speed of the electron.

The electron is experiencing uniform circular motion. The only force on it is the attractive force between the negative electron and the positive nucleus:

kZe2/r2 = mv2/r

Therefore mv2 = kZe2/r

If you rearrange Bohr's angular momentum equation to solve for the velocity:

v = nh/2pmr

and then plug that into the equation:

mv2 = kZe2/r you get:

mn2h2/4p2m2r2 = kZe2/r

Solving this for the radius of the nth orbit gives:

rn = [h2/4p2mkZe2] n2

rn = [5.29 x 10-11 m] n2

5.29 x 10-11 m is known as the Bohr radius.

So, Bohr's assumption that the angular momentum is quantized produces the result that the radii of the electron's allowed orbits are also quantized.

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