According to Bohr's theory of hydrogen atom, the speed of the electron, its energy and radius of its orbit vary with the principal quantum number n , respectively as

Step-by-step solution

According to Bohr's theory for a hydrogen-like atom, the radius of the n^ th orbit is given by r_n = a₀ n^2 Z , which implies r_n n^2 . The velocity of the electron in the n^ th orbit is given by v_n = v₀ Z n , which implies v_n 1 n . The total energy of the electron in the n^ th orbit is given by E_n = -13.6 Z^2 n^2 eV, which implies E_n 1 n^2 . Comparing these dependencies, the speed varies as 1 n , energy varies as 1 n^2 , and radius varies as n^2 . Answer: 1 n , 1 n^2 , n^2