Fraction of Surface Atoms with Excess Charge Assuming that the net charge on the

Question

Fraction of Surface Atoms with Excess Charge Assuming that the net charge on the negative tape is distributed uniformly over its surface, we can estimate the fraction of those surface atoms that have gained an excess electron or negative ion. XAMPLE Fraction of Surface Atoms with Excess Charge What fraction of the atoms on the charged surface of the tape have gained or lost charge? (Assume that an atom gains or loses at most one electron charge.) Solution Surface area of a 1-cm-wide, 20-cm-long tape: A-(0.2 m)(0.01 m) = 2 × 10-3 2 Approximate cross-sectional area occupied by an atom whose radius is approximately 1 x 10-10 m: Agton® (2 x 10-10 m)2 = 4 x 10-20 m 2 Number of atoms on the surface: Aatom = X 10-3 Number of excess electrons (or ions): 10 × 10-9c 16 x 10-19 = 5 × 1016 atoms Aatom 4x 10-20 m2 6.25 × 1010 Fraction of surface atoms with excess charge: 625 × 1010 5x1016 ~ 1 × 10-6 Thus only about one in a million atoms on the surface of the tape has acquired an excess electron or lost an electron-a small fraction. At the macroscopic level, the charge on the surface of the tape may appear to be distributed quite uniformly. At the atomic level, though, we see that the atoms with excess charge are sprinkled quite sparsely over the surface.

Explanation / Answer

The 1st one is the total charge on the tape (excess)

This must be given in the previous problem since it is not mentioned in this one.

The second one is the total number of atoms on the surface which as the solution indicates, is calculated in 1st two steps

Total charge divided by charge on single atom gives, number of atoms with any charge. (At Max 1 electron charge)

These atoms divided by total atoms gives the fraction

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