Question

The radius of first orbit of h-atom is r.then the radius of first orbit of li2+ will be

Answer 1

R=52.9×n/z
R proportional to n/Z
r/r'=1/1×3/1
r'=r/3

Answer 2

Answer: The radius of $Li^{2+}$ comes out to be $\frac{r}{3}$

Explanation:

Radius of an atom is given by the equation:

$r=\frac{0.059\times n^2}{Z}$

where,

n = number of orbit, for first n = 1, for second n = 2 and so on.

Z = Atomic number

We are given:

$r=\frac{0.059\times 1^2}{1}$      .....(1)

Taking radius of $Li^{2+}$ to be r'

$r'=\frac{0.059\times 1^2}{3}$    .....(2)

Taking ratio of 2 to 1, we get:

$\frac{r'}{r}=\left(\frac{\frac{0.059\times 1^2}{3}}{\frac{0.059\times 1^2}{1}}\right)\\\\\frac{r'}{r}=\frac{1}{3}\\\\\Rightarrow r'=\frac{r}{3}$

Hence, the radius of $Li^{2+}$ comes out to be $\frac{r}{3}$