Question

The radius of the first orbit of $H$-atom is $r$. Then the radius of the first orbit of ${Li}^{2+}$ will be:

• A. $\frac{r}{9}$
• B. $\frac{r}{3}$
• C. $3r$
• D. $9r$

Answer 1

The correct option is B $\frac{r}{3}$

Radius of any one electron system is $r=\frac{0.0529n^2}{Z}$ nm,

where n= no. of orbit, z = atomic no.

For H- atom, $z=1$ and $n=1$

Radius of first orbit of H-atom $=\frac{0.0529\times 1^2}{1}=r$

For Li, $z=3$

$L{i}^{+2}$ have the same number of electrons and orbits as in hydrogen atom.

Here $r=0.0529nm$, radius of first orbit of $L{i}^{+2}$ = $\frac{0.0529\times 1}{3}$ $=\frac{0.0529}{3}$

$=\frac{r}{3}$