question_answer

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: [JEE ONLINE 09-04-2013]

A) \[\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}\,m{{c}^{2}}}\]

B) \[\frac{4\pi {{\varepsilon }_{0}}\,{{b}^{2}}}{m{{e}^{2}}}\]

C)             \[\frac{m{{c}^{2}}}{4\pi {{\varepsilon }_{0}}\,{{b}^{2}}}\]

D) \[\frac{4\pi {{\varepsilon }_{0}}\,m{{c}^{2}}}{{{e}^{2}}}\]

Correct Answer: A

Solution :

[a] The typical atomic size given by