Question

Suppose a 1.0 -g nugget of pure gold has zero net charge. What would be its net charge after it has \(1.0 \%\) of its electrons removed?

Short answer

The net charge of the gold nugget after 1.0% of its electrons are removed would be 4.07 Coulombs.

Step-by-step solution

Calculate the number of moles of gold in the nugget

To find the number of moles of gold in the nugget, we can use the formula: moles = mass / molar mass The given mass of the gold nugget is 1.0 g, and the molar mass of gold (Au) is 197.0 g/mol. So, the number of moles of gold in the nugget is: moles = (1.0 g) / (197.0 g/mol) = 0.0051 mol

Determine the total number of electrons in the gold nugget

To find the total number of electrons in the nugget, we can use the formula: total electrons = moles × Avogadro's number × number of electrons per atom Gold has 79 electrons per atom, and Avogadro's number is approximately \(6.022×10^{23}\) atoms/mol. So, the total number of electrons in the nugget is: total electrons = (0.0051 mol) × (\(6.022×10^{23}\) atoms/mol) × (79 electrons/atom) = \(2.54×10^{25}\) electrons

Calculate the number of electrons removed

Since 1.0% of the electrons are removed, we can find the number of electrons removed by multiplying the total number of electrons by 0.01: electrons removed = (\(2.54×10^{25}\) electrons) × 0.01 = \(2.54×10^{23}\) electrons

Calculate the net charge of the gold nugget after electron removal

Finally, to find the net charge after electron removal, we need to multiply the number of electrons removed by the elementary charge (which is approximately \(1.602×10^{-19}\) C): net charge = (\(2.54×10^{23}\) electrons) × (\(1.602×10^{-19}\) C/electron) = 4.07 C After removing 1.0% of its electrons, the net charge of the gold nugget would be 4.07 C.