In hydrogen atom in its ground state, the first Bohr orbit has radius ' r₁ ^ . When the atom is raised to one of its excited states, the electrons orbital velocity becomes one-third. The radius of that orbit is

Step-by-step solution

The orbital velocity v_n 1/n and radius r_n n^2 for the hydrogen atom. Given v_ n' = v₁/3 , the velocity ratio yields 1/n' = 1/3 , so n' = 3 . The radius ratio is r_ n' /r₁ = (n')^2 = 9 . Thus, the radius is 9r₁ .