If the radius of the second Bohr orbit of a singly ionized helium atom ( He^+ ) is x , then the radius of the third Bohr orbit of a doubly ionized lithium atom ( Li²⁺ ) will be:

Step-by-step solution

The radius of the n -th Bohr orbit for a hydrogen-like species is given by r_n n^2 Z . For the second Bohr orbit of He^+ ( n = 2 , Z = 2 ): x 2^2 2 x 2 For the third Bohr orbit of Li²⁺ ( n = 3 , Z = 3 ): r 3^2 3 r 3 Taking the ratio of the two radii: r x = 3 2 r = 3 2 x Answer: 3 2 x