Show that the radius of the orbit in hydrogen atom varies as n² where n is the principal quantum number of the atom

According to Bohr's second postulate, mvr=nh/2π where m be the mass of an electron, v be the velocity and r be the radius of orbit in which the electron revolves around the nucleus. So, v=nh/2πmr Here, the centripetal force is provided by the electrostatic force of attraction between electron and nucleus. Thus, mv²/r=k(Ze)(e)/r² ⇒r=kZe²/mv² Substituting the value of v: r=n²h²/4π²mkZe² Thus, r∝n²