Question

Roughly, how does the size of a triply ionized beryllium ion compare with hydrogen?

Short answer

The Triple ionized beryllium ion is roughly $1/3^{rd}$ as compared to the radius of the hydrogen atom.

Step-by-step solution

A concept:

Ionization decreases the size of the object as the nucleus has to hold fewer electrons, hence, ionization energy increases and it becomes more difficult to remove electrons.

Radii of triply ionized beryllium ion and hydrogen:

From eq. (7-42), you get,

Radius of hydrogen like atoms is,

$r_n=\frac{\mathbf{1}}{Z}{n}^{\mathbf{2}}{a}_{\mathbf{0}\mathbf{}\mathbf{}}\dots ..\left(1\right)$

Hence, Radius of hydrogen is,

$r_n=a_{\mathbf{0}}\dots ..\left(2\right)$

And radius of beryllium ion is given by,

$r_b=\frac{1}{3}{1}^2{a}_0$

$r_b=\frac{a_{\mathbf{0}}}{3}\dots ..\left(3\right)$

Conclusion:

From equation (2) and (3) into equation (1), and you get the following.

The Triply ionized beryllium ion is roughly $1/3^{rd}$ as compared to the radius of the hydrogen atom.