Question

derive an expression relating radius of the atom to the mass, charge and orbit number of electron

Answer 1

Answer:

On the basis of Bohr's theory, derive an expression for the radius of the of the nth orbit of an electron of the world .

Let e, m and v be respectively the charge, mass and velocity of the electron and r the radius of the orbit. The positive charge on the nucleus is Ze, where Z is  the atomic number (in case of hydrogen atom Z = 1). As the centripetal force is provided by the electrostatic force of attraction. We have

rmv2=4πε01r2(Ze)×e

mv2=4πε0rZe2  ....(i)

From the first postulate, the angular momentum of the electron is

mvr=n2πh  ....(ii)

where n (= 1, 2, 3, ...) is quantum number. Squaring eq. (ii) and dividing by eq. (i), we 

get 

r=n2πmZe2h2ε0

Z=1

Since

r=n2πme2h2ε0