Question

Which hydrogen like species will have same radius as that of Bohr orbit hydrogen atom?

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

Answer 1

Answer: (C)

Radius of orbit $(r)=\frac{n^2{h}^2}{4{\pi }^{2}m{e}^2}\times \frac{1}{Z}$
In it $h,\pi ,m$ and $e$ are constants, so after substituting these values, we get
$r=\frac{0.529n^2}{Z}\mathring{A}$
$Z=1\text{ for }H$
$\therefore r_H=\frac{0.529n^2}{1}\mathring{A}$.....(i)
The transition from $n=2$ to $n=1$ in $H$-atom will have the same wavelength as the transition from $n=4$ to $n=2$ in $H{e}^{+}$ion.