Structure Of Atom Question 4
Question 4 - 25 January - Shift 1
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
(1) $\frac{9}{4} x$
(2) $\frac{4}{9} x$
(3) $\frac{27}{16} x$
(4) $\frac{16}{27} x$
Show Answer
Answer: (3)
Solution:
Formula: Bohr’s Radius of Hydrogen like Atoms
$Li^{2+}$ $Be^{3+}$ $r_2=x=k \times \frac{2^{2}}{3}=\frac{4 k}{2}$ $r_3=y=k \times \frac{3^{2}}{4}$
$\frac{y}{x}=\frac{9}{4} \times \frac{3}{4}=\frac{27}{16}$
$y=\frac{27}{16} x$
