Which state of triply ionised beryllium ( B e 3 + ) has the same orbital radius as that of ground state of hydrogen?

Step-by-step solution

Radius of orbit of electron in n th excited state of hydrogen r = ε 0 h 2 n 2 π m Z e 2 ∴ r ∝ n 2 Z … ( i ) ∴ r 1 r 2 = n 1 2 n 2 2 × Z 2 Z 1 But r 1 = r 2 So, n 2 2 = n 1 2 × Z 2 Z 1 Here, n ⁡ 1 = 1(ground state of hydrogen), Z ⁡ 1 = 1(atomic number of hydrogen), Z ⁡ 2 = 4(atomic number of beryllium) ∴ n 2 2 = 1 2 × 4 1 or n 2 2 = 4 or n ⁡ 2 = 2