Question

ratio of the radius of first orbit of He+ to the second orbit of Li2+ is
1. 1:4
2. 2:3
3. 3:8
4. 2:9

Answer 1

He:li

We will use the formula [r=k/z] And here k=1

He= 1/2 : Li= 1/3 your ratio is 2:3

I might not be able to explain my answer but answer is correct

Answer 2

Answer:

The correct option is 3.

Explanation:

$r_n=\frac{0.53\times 10^{10}\times n^2}{Z}$

$r_n$ = radius of the nth shell

Z = Atomic number

Radius of first orbit of $He^+$

n=1, Z = 2

$r_{1}=\frac{0.53 \times 10^{10}\times 1^2}{2}$..(1)

Radius of second orbit of $Li^{2+}$

n=2, Z = 3

$R_{2}=\frac{0.53 \times 10^{10}\times 2^2}{3}$..(2)

Dividing (1) to (2):

$\frac{r_{1}}{R_{2}}=\frac{\frac{0.53 \times 10^{10}\times 1^2}{2}}{\frac{0.53 \times 10^{10}\times 2^2}{3}}=\frac{3}{8}$

Hence, the correct option is 3.