Question

If $\alpha =\frac{h}{4 \pi ^{2} m e^{2}},$ then the correct expression to calculate of the circumference of the first orbit of hydrogen atom is

• A. $\sqrt{4}\pi hα$
• B. $\sqrt{2}\pi hα$
• C. $\sqrt{4 h^{2}}\pi α$
• D. Both A and C

Answer 1

Answer: (D)

circumference $=2\pi r$

$2\times \pi \times \frac{n^{2} h^{2}}{4 \pi ^{2} m Z e^{2}}$

$n=1$

$Z=1$

and $\frac{h}{4 \pi ^{2} me^{2}}=\alpha $

Thus, $2\times \pi \times r$

$=\sqrt{4}\pi hα$

or $\sqrt{4 h^{2}}\pi α$