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Chapter 20: Problem 38

A 2 -g ping-pong ball rubbed against a wool jacket acquires a net positive charge of \(1 \mu \mathrm{C}\). Estimate the fraction of the ball's electrons that have been removed.

Short Answer

Expert verified
The short answer will be the numerical value obtained from the equation for the fraction of the ball鈥檚 electrons that have been removed, as derived in Step 3.

Step by step solution

01

Calculate the number of electrons in 2 grams of the ping-pong ball

A ping-pong ball is primarily made of cellulose (wood pulp) but for simplicity, we will assume it's made of carbon whose atomic mass is approximately 12 amu. The number of atoms in an element can be calculated according to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms per mole. Since one carbon atom has 6 electrons, the number of electrons in 2 grams of carbon can be calculated as follows: \n\(No.\, of\, electrons\, in\, 2g\, carbon = \frac{2 \,g\, carbon}{12 \,g/mol} \times 6.022 \times 10^{23} \,atoms/mol \times 6\, electrons/atom\)
02

Calculate the number of electrons corresponding to the charge of \(1 \mu C\)

Knowing that the charge of one electron is approximately \(1.6 \times 10^{-19}\) Coulombs, the number of electrons that will generate a charge of \(1 \mu C\) can be calculated as follows: \n\(No. \,of\, electrons\, in\, 1 \mu C\, = \frac{1 \mu C}{1.6 \times 10^{-19}}\)
03

Determine the fraction of the ball鈥檚 electrons that had been removed

The fraction of the ball鈥檚 electrons that have been removed to result in a charge of \(1 \mu C\) is obtained by taking the ratio of the number of electrons in \(1 \mu C\) to the number of electrons in 2 grams of carbon. \n\(Fraction\, of\, removed\, electrons = \frac{No.\, of\, electrons\, in\, 1 \mu C}{No.\, of\, electrons\, in\, 2g\, carbon}\)

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