Answer:
The correct answer is option D.
Explanation:
Formula used for the radius of the [tex]n^{th}[/tex] orbit will be,
[tex]r_n=\frac{n^2\times 52.9}{Z}[/tex] (in pm)
where,
[tex]r_n[/tex] = radius of [tex]n^{th}[/tex] orbit
n = number of orbit
Z = atomic number
Radius of the first orbit, n = 1
[tex]r_1=\frac{1^2\times 52.9}{Z}=\frac{1\times 52.9}{Z}[/tex]..[1]
Radius of the third orbit, n = 3
[tex]r_3=\frac{3^2\times 52.9}{Z}=\frac{9\times 52.9}{Z}[/tex]..[2]
[1] ÷ [2]
[tex]\frac{r_1}{r_3}=\frac{\frac{1\times 52.9}{Z}}{\frac{9\times 52.9}{Z}}[/tex]
[tex]r_1\times 9=r_3[/tex]
The radius of the 3rd orbit is nine times the radius of first orbit.
