Question

ratio of radius of first three orbits of lithium + 2 Ion will be​

Answer 1

we have to find ratio of radius of first three orbits of Lithium ion, Li²+.

from Bohr's theory,

radius of nth orbit is given by, $\bf{r_n=0.529\frac{n^2}{\mathbb{Z}}}$ A° where n is orbit number and Z is atomic number.

so, radius of first orbit , n = 1

$r_1$ =0.529 × 1²/(3) = 0.529/3 A°

radius of 2nd orbit, n = 2,

$r_2$ = 0.529 × (2)²/3 = 0.529 × 4/3 A°

radius of 3rd orbit , n = 3

$r_3$ = 0.529 × (3)²/3 = 0.529 × 9/3 A°

now, $r_1:r_2:r_3$ = 0.529/3 : 0.529 × 4/3 : 0.529 × 9/3

= 1 : 4 : 9

hence, ratio of radius of first three orbits of lithium ion will be 1 : 4 : 9.