The radius of which of the following orbit is same as that of the first Bohr's orbit of hydrogen atom.

Options

A. `He^+ (n = 2)`
B. `Li^(2+) (n = 2)`
C. `Li^(2+) (n = 3)`
D. `Be^(3+) (n = 2)`

Answer

D

Explanation

Radius of an orbit, `r = (0.529 n^2)/(Z) Å`
For H atom Z = 1
`r_1 = 0.529 n^2 Å`
For `Be^(3+), Z = 4`
`r_(Be^(3+)) = (0.529 n^2)/4 Å` Given that `r_H = r_(Be^(3+))`
`:.` It is equal when n = 2 for `Be^(3+)`
`:. r_2 (Be^(3+)) = r_1 (H)`