The radius of 2 nd orbit of He + of Bohr's model is r 1 and that of fourth orbit of Be 3 + is represented as r 2 . Now the ratio r 2 r 1 is x : 1 . The value of x is _____.

Step-by-step solution

The formula to calculate the radius r of any n th Bohr's orbit is given by r = r 0 n 2 Z       . . . 1 where, r 0 is Bohr's radius, n is the principal quantum number and Z is the atomic number. Thus, for Helium ion, r 1 = r 0 2 2 2 =   2 r 0       . . . 2 And, for the Beryllium ion, r 2 = r 0 4 2 4 = 4 r 0       . . . 3 Divide equation (3) by equation (2) to obtain the required ratio. r 2 r 1 = 4 r 0 2 r 0 = 2 Hence, x = 2 .