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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# What net charge would you place on a 100 g piece of sulfur if you put an extra electron on 1 in 1012 of its atoms? (Sulfur has an atomic mass of 32.1.)

If sulfur has an extra 1 electron in 1012 of its atoms, then the net charge on 100 g piece is $-0.300\mu C$.

See the step by step solution

## Step 1: Given Data

• Mass of piece of sulphur is 100 g
• Fraction of extra electrons is $\frac{1}{{10}^{12}}$
• Atomic mass of sulphur is 32.1

## Step 2: Charged body

When there is imbalance in the number of electron and proton in a body, then it is said to be charged. If a body gains extra electron, the body is said to be negatively charged.

## Step 3: Number of extra electrons

The number of moles of sulfur is,

$N=\frac{m}{M}$

Here, N is the number of moles of sulfur, m is the mass of the sulfur piece (m = 100 g) , and is the molar mass of the sulfur ( M = 32.1 g ) .

Substituting all known values,

$N=\frac{100g}{32.1g}\phantom{\rule{0ex}{0ex}}=3.115$

The number of sulfur atom is,

${N}_{a}=\left(3.115\right)×\left(6.022×{10}^{23}\right)\phantom{\rule{0ex}{0ex}}=1.876×{10}^{24}$

Since, there is 1 extra electron on every 1012 atom. Therefore, the number of extra electrons is,

$n=\frac{1.876×{10}^{24}}{{10}^{12}}\phantom{\rule{0ex}{0ex}}=1.876×{10}^{12}$

## Step 4: Net charge

According to the quantization of charge,

Q = ne

Here, Q is the net charge, n is the number of extra electron $\left(n=1.876×{10}^{12}\right)$ , and e is the charge on an electron $\left(e=-1.6×{10}^{-19}\mathrm{C}\right)$ .

Substituting all known values,

$Q=\left(1.876×{10}^{12}\right)×\left(-1.6×{10}^{-19}C\right)\phantom{\rule{0ex}{0ex}}=3.00×{10}^{-7}C×\left(\frac{1\mu C}{{10}^{-6}C}\right)\phantom{\rule{0ex}{0ex}}=-0.300\mu C$

Hence, the net charge on 100 g of piece of sulfur, if it has an extra 1 electron in 1012 of its atoms, is $-0.300\mu C$ .