Question

Circumference of the first orbit of hydrogen atom is given by the formula: $[a_0=\frac{h^2}{4{\pi }^2{me}^2}]$

• A. $\frac{22}{7}{a}_0$
• B. $\frac{\pi a_0}{2}$
• C. $\sqrt{4}\pi a_0$
• D. $\pi a_0$

Answer 1

The correct option is C $\sqrt{4}\pi a_0$

$Circumference=2\pi r$

We have,

$r=\frac{h^2\times n^2}{4{\pi }^{2}m{e}^2}.\frac{1}{Z^2}$

Hydrogen atom with $Z=1$ and $n=1$ radius is given by,

$r=\frac{h^2}{4{\pi }^{2}m{e}^2}$$=a_0$

Therefore,

$Circumference=2\pi a_0$$=\sqrt{4}\pi a_0$