In hydrogen atom, electron excites from ground state to higher energy state and its orbital velocity is reduced to ( 1 3 )^ rd of its initial value. The radius of the orbit in the ground state is R . The radius of the orbit in that higher energy state is

Step-by-step solution

where subscripts h and g denotes higher energy state and ground state. Orbital velocity of electron in the n^ th orbit is v_n= e^2 2 ₀ n h or v_n 1 n Equating eqns. (i) and (ii), we get n=3 Radius of n^ th orbit is r_n= n^2 h^2 ₀ e^2 m^2 or r_n n^2 aligned r₃ r₁ & = (3)^2 (1)^2 =9 r₃ & =9 r₁=9 R ( r₁=R( Given ) ) aligned