Electrons revolve around the nucleus in an atom. The path of these electrons is fixed and is known as orbits or shells. The centripetal force, which is due to the attraction of positively charged nucleus and negatively charged electrons, is balanced by centrifugal force produced by the circular motion of electrons around the nucleus. That is why electrons do not fall in the nucleus.
According to Bohr’s atomic model, these two forces are equal and opposite to each other. The electrons move in a fixed path and the radius is given by,
Fe = Fc (i)
Fe = kZq1q2 / r2 (ii)
Fe is the electrostatic force
Z is the atomic number
q1 is the charge of the nucleus
q2 is the charge on the electron
k is the electrostatic constant
Fc = mv2/ r (iii)
Fc is the centrifugal force
m is the mass of the electron
r is the distance of the electron from the nucleus
Now, putting values from equations (ii) and (iii) in equation (i) and rearranging, we get,
r = kZe2/ mv2 (iv)
In the case of hydrogen, where Z =1, the radius of the hydrogen atom comes out to be 0.529 Å (10-10 m).
This means the electrons in hydrogen atoms will revolve around the nucleus at a fixed radius of 0.529 Å. Therefore, it cannot fall into the nucleus.
Similar to hydrogen atoms, electrons of all other atoms have a fixed trajectory too, having a fixed radius and that can be calculated by this equation.
r = kZe2/ mv2