From the following, the quantity (constructed from the basic… | JEE Main 2013 (9 Apr, Shift 1)

Q74JEE Main 2013 · 9 APR · SHIFT 1Medium

Applications of Dimensional Analysis

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:

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Answer: (a)

$\dfrac{e^2}{4\pi\epsilon_0 r}$ is an energy, so $\dfrac{e^2}{4\pi\epsilon_0 m_ec^2}$ is (energy $\times$ length)/energy $=$ length.
The other options do not have the dimension of length.
Its value $\approx 2.8\times10^{-15}$ m, the classical electron radius, which is a sub-atomic length scale.
So the answer is (a).

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Applications of Dimensional Analysis question from JEE Main 2013 (9 Apr, Shift 1)

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