Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

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 $1.48 \times 10^{8} C$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Data

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

Each atom of plutonium has 94 protons.

Step 2: Quantization of charge

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.

Step 3: Total number of protons

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,

$N = \frac{(4.00 k g)}{(244 g)} = \frac{(4.00 k g) \times (\frac{1000 g}{1 k g})}{(244 g)} = 16.39$

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,

$N_{a} = (16.39) \times (6.022 \times 10^{23}) = 9.87 \times 10^{24}$

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

$n = (94) \times (9.87 \times 10^{24}) = 9.28 \times 10^{26}$

Step 4: Net charge

According to the quantization of charge,

$Q = n |q_{e}|$

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

Substituting all known values,

$Q = (9.28 \times 10^{26}) \times (1.6 \times 10^{- 19} C) = 1.48 \times 10^{8} C$

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

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College Physics (Urone)

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Short Answer

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?

Step by Step Solution

Step 1: Given Data

Step 2: Quantization of charge

Step 3: Total number of protons

Step 4: Net charge

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College Physics (Urone)

Answers without the blur.

Short Answer

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?

Step by Step Solution

Step 1: Given Data

Step 2: Quantization of charge

Step 3: Total number of protons

Step 4: Net charge

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