# The ratio of the radii of first orbit of H, He+ and Li2+ is?

Jun 13, 2017

The radii are in the ratio $6 : 3 : 2$.

#### Explanation:

The radii of the first orbits of a hydrogen-like ion are given by the equation

r = (ħ^2)/(Zm_ek_ee^2)

Since everything except $Z$ is constant, we can rewrite the formula as

$r = \frac{k}{Z}$

Then the ratios of the three radii for $Z = 1 , 2$ and $3$ are

${r}_{1} : {r}_{2} : {r}_{3} = \frac{1}{1} : \frac{1}{2} : \frac{1}{3} = 6 : 3 : 2$