a. What is the total negative charge, in coulombs, of all the electrons in a small 0.950 g sphere...

Question:

a. What is the total negative charge, in coulombs, of all the electrons in a small 0.950 g sphere of carbon? One mole of carbon is 12.0 g, and each atom contains 6 protons and 6 electrons.

b. Suppose you could take out all the electrons and hold them in one hand, while in the other hand you hold what is left of the original sphere. If you hold your hands 1.40 m apart at arm's length, what force will each of them feel?

c. Will it be attractive or repulsive? Explain.

Electrical Forces and Type of Charges:

All elements have an equal number of protons and electrons, which is why elements are neutral. It's also the reason why electrons stay around the nucleus. Electrical forces arise from charges interacting, where charges of the same type repulse and push each other away while charges of the opposite type attract and pull each other closer.

Answer and Explanation: 1

a. The total negative charge on the sphere of carbon is equal to the sum of all the electrons in the sphere. Each carbon atom in the sphere has six atoms, and the whole sphere is composed of a certain amount of moles that, when multiplied by Avogadro's number, gives the total number of atoms.


The number of moles of the carbon sphere:

{eq}Moles = \frac {Mass}{Molar~mass} \\ Moles = \frac {0.950g}{12.0g/mol} \\ Moles = 0.0792mol {/eq}


The number of carbon atoms in the sphere:

The number of carbon moles * Avogadro's number

{eq}0.0792mol \times 6.02 \times 10^{23}mol^{-1} \\ 4.77 \times 10^{22}~carbon~atom {/eq}


The number of electrons in the sphere:

The number of carbon atoms in the sphere * The number of electrons in each carbon atom

{eq}4.77 \times 10^{22}~carbon~atom \times 6~electrons \\ 2.86 \times 10^23~electron {/eq}


The total negative charge of all the electrons in the sphere:

The number of electrons in the sphere * The charge of an electron

{eq}2.86 \times 10^{23} \times 1.60 \times 10^{-19}C \\ 4.58 \times 10^4C {/eq}



b. If all the electrons in the carbon atoms were separated, all the would be left is the nucleus, which contains protons and neutrons. Neutrons are not charged, while protons are positively charged. Separating the electrons in one hand and the nucleus in another hand means one hand will be negatively charged, and the other will be positively charged. Therefore, each hand will exert an electrical force on the other. The magnitude of the electrical force can be calculated using Coulomb's law. Since there are as many protons as electrons and a proton and an electron have the same magnitude of charge, each hand's overall charge will be the same but different in type.


The electrical force each hand exerts on the other:

{eq}F = k \frac {q_1q_2}{r^2} {/eq}


-F: the electrical force

-k: Coulomb constant = {eq}8.99 \times 10^9N.m^2.C^{-2} {/eq}

-q1 and q2: the value of the two charges

-r: the distance between the charges


{eq}F = 8.99 \times 10^9N.m^2.C^{-2} \times \frac {(1.60 \times 10^{-19}C) \times (1.60 \times 10^{-19}C)}{(1.40m)^2} \\ F = 8.99 \times 10^9N.m^2.C^{-2} \times \frac {2.56 times 10^{-34}C^2}{1.96m^2} \\ F = \frac {2.30 \times 10{-24}N.m^2}{1.96m^2} \\ F = 1.17 \times 10^{-24}N {/eq}


That means each hand exerts a force with a magnitude of {eq}1.17 \times 10^{-24}N {/eq} on the other hand.



c. Considering that each hand contains particles with one type of charge that is opposite to the other type of charge on the other hand, the two hands will surely exert attraction forces on each other.


Learn more about this topic:

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Calculating Electric Forces, Fields & Potential

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Chapter 7 / Lesson 6
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From electric charges come electric forces and electric fields. In this lesson, we will explore how to calculate electric forces between charges, electric fields generated by them, and electric potentials in specific locations because of them.


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