Question

Which orbit of the triply ionized beryllium $\left(B{e}^{3+}\right)$ has the same orbit radius as that of the ground state of hydrogen atom?

• A. $n=2$
• B. $n=3$
• C. $n=1$
• D. $n=4$

Answer 1

The correct option is A $n=2$

The radius of ground state of hydrogen atom = $0.529\stackrel{o}{A}$
Let the lone electron of the triply-ionized $B{e}^{3+}$ correspond to the level $n$
From the given data, both the above radii are equal.
So,
$0.529=0.529\times \frac{n^2}{Z}$
$\Rightarrow 0.529=0.529\times \frac{n^2}{4}$
[atomic number of $Be=4(Z=4)$]
$\therefore n=2$