Solving Elementary Charges Homework: Find # Electrons Transferred

In summary, two spheres with charges -3q and +5q were brought into contact and then separated by a distance of 1.5 m, resulting in a force of 8.1 X 10^-2 N between them. By using Coulomb's law, it can be determined that 1.1 X 10^4 electrons were transferred from one sphere to the other, with the negative charge flowing towards the positive charge.
  • #1
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Homework Statement


Sphere A with charge -3q is 1.5 m from another identical sphere B with charge +5q. The two spheres are broughtinto contact and then separated by a distance of 1.5 m; the magnitude of the force between the spherees is 8.1 X 10^-2 N.
a. Find the number of electrons transferred from one sphere to the other. Explain which way they moved.


Homework Equations


Q=Ne (e=1.602 X 10^-19)


The Attempt at a Solution


I don't really understand the problem. What does it mean when it says that "the two spheres are brought into contact and then separated...". Do i take the average of the charges? The answer for the number of electrons is 1.1 X 10^4. Please help.
 
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  • #2
What will happen when the two spheres come together? One has positive charge and one has negative charge. Hmm, do you think that maybe charge will flow? Which direction?

Use Coulomb's law which is:

[tex] F= \frac {Q_1 Q_2} {4 \pi \epsilon d^2} [/tex]

to get the absolute amount of charge of different sign. Keep in mind that the charge that moves will combine with the positive charge and isn't counted.
 
  • #3


As a scientist, it is important to carefully read and understand the problem before attempting to solve it. In this case, the problem is describing a situation where two spheres with opposite charges are brought into contact and then separated. This means that the charges on the spheres will redistribute due to the contact and repulsion between the like charges.

To solve for the number of electrons transferred, we can use the equation Q=Ne, where Q is the total charge, N is the number of electrons, and e is the elementary charge. We can also use the equation F=kQ1Q2/r^2 to find the magnitude of the force between the spheres, where k is the Coulomb's constant, Q1 and Q2 are the charges on the spheres, and r is the distance between them.

Using the given information, we can set up the following equations:
Q1 = -3q
Q2 = +5q
r = 1.5 m
F = 8.1 X 10^-2 N

From the equation F=kQ1Q2/r^2, we can solve for the total charge on the spheres:
8.1 X 10^-2 = (9 X 10^9)(-3q)(+5q)/(1.5)^2
Solving for q, we get q = 1.6 X 10^-19 C.

Now, to find the number of electrons transferred, we can use the equation Q=Ne and solve for N:
1.6 X 10^-19 = N(1.602 X 10^-19)
N = 1.1 X 10^4 electrons.

This means that 1.1 X 10^4 electrons were transferred from one sphere to the other during the contact and separation process. Since the force between the spheres is repulsive, we can infer that the electrons moved from the sphere with a negative charge (-3q) to the sphere with a positive charge (+5q).

To better understand this concept, you can think of it as the electrons being "pulled" towards the positively charged sphere during contact, and then "pushed" away from it as the spheres are separated. This redistribution of charges results in a net force between the spheres, which we can calculate using Coulomb's law.

I hope this explanation helps you understand the problem and solve it successfully. Remember to always carefully read and understand the problem before
 

1. How do I determine the number of electrons transferred in a chemical reaction?

The number of electrons transferred in a chemical reaction can be determined using the following equation:

Number of electrons transferred = (oxidation state of the atom after reaction) - (oxidation state of the atom before reaction)

2. What is an oxidation state?

An oxidation state is a measure of the degree of oxidation of an atom in a chemical compound. It indicates the number of electrons that an atom has gained or lost in order to form a chemical bond.

3. How do I calculate the oxidation state of an atom?

The oxidation state of an atom can be calculated by following a set of rules based on the type of compound and the elements present. For example, in a neutral compound, the oxidation states of all atoms must add up to zero. In an ion, the oxidation states of all atoms must add up to the overall charge of the ion.

4. Can the number of electrons transferred be negative?

Yes, the number of electrons transferred can be negative. This indicates that electrons were gained by an atom during the reaction instead of being lost.

5. What is the significance of determining the number of electrons transferred in a chemical reaction?

Determining the number of electrons transferred in a chemical reaction is important because it helps to identify the type of reaction that has occurred (e.g. oxidation-reduction), and it also allows for the balancing of the chemical equation by ensuring that the number of electrons gained equals the number of electrons lost.

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