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Q9PE

Expert-verifiedFound in: Page 664

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**How many coulombs of positive charge are there in 4.00 kg of plutonium, given its atomic mass is 244 and that each plutonium atom has 94 protons?**

4.00 kg of plutonium has a net charge of $1.48\times {10}^{8}\mathrm{C}$.

- Mass of plutonium (m) = 4.00 kg.
- Atomic mass of plutonium is 244.

- Each atom of plutonium has 94 protons.

According to the quantization of charge, every charged body is made of fundamental units of charge (electrons and protons). The net charge on the charged body equals the integral multiple of this fundamental charge.

The number of moles of the plutonium atom is,

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

Here, *N* is the number of moles of the plutonium, *m* is the mass of the plutonium (*m = 4.00 kg)*, and is the molar mass of the plutonium (M = 244 g).

Substituting all known values,

$N=\frac{\left(4.00kg\right)}{\left(244g\right)}\phantom{\rule{0ex}{0ex}}=\frac{\left(4.00kg\right)\times \left(\frac{1000g}{1kg}\right)}{\left(244g\right)}\phantom{\rule{0ex}{0ex}}=16.39$

Since one mole of a substance contains $6.022\times {10}^{23}$ elementary entities of the given substance. Therefore, the total number of atoms in 4.00 kg of plutonium is,

${N}_{a}=\left(16.39\right)\times \left(6.022\times {10}^{23}\right)\phantom{\rule{0ex}{0ex}}=9.87\times {10}^{24}$

We know that one atom of plutonium contains **94** protons. Therefore, the total number of protons in 4.00 kg of plutonium is,

$n=\left(94\right)\times \left(9.87\times {10}^{24}\right)\phantom{\rule{0ex}{0ex}}=9.28\times {10}^{26}$

According to the quantization of charge,

$Q=n\left|{q}_{e}\right|$

Here, Q is the net charge, *n* is the number of protons in 4.00 kg of plutonium $\left(n=9.28\times {10}^{26}\right)$ , and $\left|{q}_{e}\right|$ is the fundamental unit of charge $\left(\left|{q}_{e}\right|=1.6\times {10}^{-19}C\right)$.

Substituting all known values,

$Q=\left(9.28\times {10}^{26}\right)\times \left(1.6\times {10}^{-19}C\right)\phantom{\rule{0ex}{0ex}}=1.48\times {10}^{8}C$

Hence, the net charge on 4.00 kg of plutonium is $1.48\times {10}^{8}C$.

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