Question 138 of 149
From the following, the quantity (constructed from the basic constants of nature), that has the dimensions, as well as correct order of magnitude, vis-a-vis typical atomic size, is:
Show answer and solution
Answer: (A)
As
also
Therefore dimensionally
$\begin{aligned}
& \mathrm{mc}^2=\frac{1}{4 \pi \epsilon_0} \frac{\mathrm{q}^2}{\mathrm{r}} \\
& \Rightarrow \mathrm{r}=\frac{\mathrm{e}^2}{4 \pi \epsilon_0 \mathrm{mc}^2}
\end{aligned}$
also
Therefore dimensionally
$\begin{aligned}
& \mathrm{mc}^2=\frac{1}{4 \pi \epsilon_0} \frac{\mathrm{q}^2}{\mathrm{r}} \\
& \Rightarrow \mathrm{r}=\frac{\mathrm{e}^2}{4 \pi \epsilon_0 \mathrm{mc}^2}
\end{aligned}$
