The radius of the n^ th stationary orbit of a hydrogen atom is R . The radius of the (n+2)^ th stationary orbit of the same atom is 2.25 R . The value of n is

Step-by-step solution

The radius of the n^ th Bohr orbit of a hydrogen atom is given by r_n n^2 . Given that the radius of the n^ th orbit is R and the radius of the (n+2)^ th orbit is 2.25 R . Taking the ratio of the radii: r_ n+2 r_n = (n+2)^2 n^2 Substitute the given values: 2.25 R R = ( n+2 n )^2 2.25 = ( n+2 n )^2 Taking the square root on both sides: 1.5 = n+2 n 3 2 = n+2 n 3n = 2n + 4 n = 4 Answer: 4