Derivation of Bohr Radius

Derivation of Bohr Radius

Let mass of an electron = m
Tangential velocity of electron = v cm/sec
Radius of orbit = r
Charge on electron = −e
Charge on proton = +e
Atomic number of the element = Z

1. Calculate the radius of 1st, 2nd and 3rd Bohr's Orbit of hydrogen.
2. Calculate the radius ratio of 3rd and 5th orbit of He⁺.
3. Calculate the radius ratio of 2nd orbit of hydrogen and 3rd orbit of Li⁺².

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Answer: 1- 0.529 Å, 2.116 Å and 4.761 Å, 2- 9:25, 3- 4:3