In hydrogen atoms, radius of the smallest orbit of the electron is a₀ , the radius of the third orbit is

Step-by-step solution

Concept: Bohr orbit radius The electron undergoes a uniform circular motion in Bohr's orbit. The coulombic attraction of the nucleus balancing the centrifugal force: mv ^2 r = eZ 4 ₀ r ^2 Further, the angular momentum of electron in Bohr's orbit is: mvr = nh 2 On squaring the second equation and dividing it by the first equation: r n^2 Z The smallest Bohr orbit has radius a ₀ as n =1 . Using the above functional dependence of the Bohr orbit, the third orbit is has radius 9 a ₀ .