Question

The ratio of radii of first orbits of $H$, ${He}^{+}$ and ${Li}^{2+}$ is:

• A. $1:2:3$
• B. $6:3:2$
• C. $1:4:9$
• D. $9:4:1$

Answer 1

The correct option is B $6:3:2$

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

$r=\frac{n^2}{Z{m}_e{k}_e{e}^2}$

since everything except 2 is constant,

$r=\frac{K}{Z}$ $(k=\frac{n^2}{m_e{k}_e{e}^2})$

Then the ratio of 3 radii for n=1,2 and 3 are

$r_1:r_2:r_3=\frac{1}{1}:\frac{1}{2}:\frac{1}{3}=6:3:2$

Hence, the correct option is $B$