Question

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

• A. $n=2, Li ^{2+}$
• B. $n=2, Be ^{3+}$
• C. $n=2, He ^{+}$
• D. $n=3, Li ^{2+}$

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
$r =\frac{0.529 n^2}{Z} \mathring{A}$
$Z =1 \text { for } H $
$\therefore r_H =\frac{0.529 n^2}{1} \mathring{A}$.....(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 $He ^{+}$ion.