Question

Which hydrogen like species will have the same radius as that of Bohr's first orbit of hydrogen atom?

• A. $n=3,L{i}^{2+}$
• B. $n=2,H{e}^{+}$
• C. $n=2,B{e}^{3+}$
• D. $n=2,L{i}^{3+}$

Answer 1

The correct option is C $n=2,B{e}^{3+}$

Radius $\left(r_n\right)=\frac{n^2{a}_0}{Z}$
For Bohr's orbit of H-atom, $Z=1,n=1$
$\therefore r_1=a_0$
$\begin{array}{cc}\text{(a)}n=3,L{i}^{2+}(Z=3)& r_2=\frac{9a_0}{3}=3a_0\\ \text{(b)}n=2,H{e}^{+}(Z=2)& r_2=\frac{4a_0}{2}=2a_0\\ \text{(c)}n=2,B{e}^{3+}(Z=4)& r_2=\frac{4a_0}{4}=a_0\\ \text{(d)}n=2,L{i}^{3+}(Z=3)& r_2=\frac{4a_0}{3}\end{array}$
So radius of second orbit $(n=2)$ for $B{e}^{3+}$ has the same radius as that of Bohr's first orbit of H-atom