Question

If the radius of the second stationary orbit of $H-$ atom is $R$ meters. Then radius of the 3rd orbit of $B^{+4}$ ion is:

• A. 2.25 $R$
• B. 0.65 $R$
• C. 0.45 $R$
• D. 0.33 $R$

Answer 1

Answer: (C)

0.45 $R$

If the radius of the second stationary orbit of H- atom is R meters. Then radius of the 3rd orbit of $B^{+4}$ ion is 0.45 R
The radius $r\propto \frac{n^2}{Z}$

For the radius of the second stationary orbit of H− atom

$R\propto \frac{2^2}{1}$
$R\propto 4$ ......(1)
For the radius of the 3rd orbit of $B^{+4}$ ion
$r\propto \frac{3^2}{5}$
$r\propto 1.8$.....(2)
Divide equation (2) by (1)
$\frac{r}{R}=\frac{1.8}{4}$
$r=0.45R$