Question

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

Answer 1

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 = k/Z`

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

`r_1:r_2:r_3 =1/1:1/2:1/3 = 6:3:2`