The ratio of the speed of electron in the 4^ th orbit of Li ⁺⁺ to the speed of electron in the ground state of hydrogen atom will be:

Step-by-step solution

The speed of an electron in the n^ th orbit of a hydrogen-like atom with atomic number Z is given by the formula v_n = v₀ Z n , where v₀ is the speed of an electron in the ground state of the hydrogen atom ( Z=1, n=1 ). For the 4^ th orbit of Li ⁺⁺ , the atomic number Z = 3 and the orbit number n = 4 . The speed of the electron in this orbit is v_ Li = v₀ 3 4 . The speed of the electron in the ground state of the hydrogen atom is v_H = v₀ 1 1 = v₀ . The ratio of the speed of the electron in the 4^ th orbit of Li ⁺⁺