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  • Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? (a) construct a quantity with the dimensions

Q 12.14     Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not,say,  thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (\approx 10^{-10}m).

    (a)    construct a quantity with the dimensions of length from the fundamental constants e, me, and c. Determine its numerical value.

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Using dimensional analysis we can see that the quantity to be constructed and consisting of me, e and c will also have \epsilon _{0} and will be equal to

\frac{e^{2}}{\epsilon _{0}m_{e}c^{2}} and has numerical value 3.5\times10-14 which is much smaller than the order of atomic radii.

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Sayak

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