Question

Which of the following expressions has the correct units to represent the radius of a hydrogen atom in its ground state?

• A. ${\epsilon }_0{h}^2/\pi m_e{e}^2$
• B. $h^2{m}_e{e}^2/4\pi {\epsilon }_0$
• C. $m_e{c}^2/h^2{e}^4$
• D. $e^4{m}_e/8{\epsilon }_0^2{h}^2$

Answer 1

The correct option is A ${\epsilon }_0{h}^2/\pi m_e{e}^2$

Radius of nth orbit of hydrogen atom is given by $r_n=\frac{n^2}{m_e}{\left(\frac{h}{2\pi }\right)}^2\left(\frac{4\pi {\epsilon }_0}{e^2}\right)$.
For ground state, $n=1$
$\therefore r_1=\frac{{\epsilon }_0{h}^2}{\pi m_e{e}^2}$.