Question

The radius of the $2^{\text {nd }}$ orbit of $Li ^{2+}$ is $x$. The expected radius of the $3^{\text {rd }}$ orbit of $Be ^{3+}$ is

• A. $\frac{16}{27} \pi$
• B. $\frac{4}{9} x$
• C. $\frac{9}{4} x$
• D. $\frac{27}{16} x$

Answer 1

Answer: (D)

$Li ^{2+}$
$r_2= x = k \times \frac{2^2}{3}=\frac{4 k }{2}$
$ Be ^{3+}$
$ r _3= y = k \times \frac{3^2}{4}$
$ \frac{y}{x}=\frac{9}{4} \times \frac{3}{4}=\frac{27}{16} $
$ y=\frac{27}{16} x$