Question

If radius of second Bohr orbit of the $He ^{+}$ion is $105.8$ $pm$, what is the radius of third Bohr orbit of $Li ^{2+}$ ion?

• A. $158.7\,\mathring{A}$
• B. $158.7 \,pm$
• C. $15.87\, pm$
• D. $1.587 \,pm$

Answer 1

Answer: (B)

$\frac{\left( r _{3}\right)_{ L ^{+2}}}{\left( r _{2}\right)_{ He ^{+}}}=\frac{ n _{1}^{2}}{ n _{2}^{2}} \times \frac{ Z _{2}}{ Z _{1}}$
$\frac{\left( r _{3}\right)_{ L ^{+2}}}{105.8\, pm }=\frac{3 \times 3}{2 \times 2} \times \frac{2}{3}$
$\left( r _{3}\right)_{ Li ^{+2}}=158.7\, pm$