Finding the mass after gaining elctrons

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In summary, the person scuffing their feet on a wool rug on a dry day accumulates a net charge of -73 µC, which is equivalent to 4.5x10^14 excess electrons. To determine the increase in mass, one must calculate the rest mass of an electron and use it along with the number of excess electrons to determine the total mass gained.
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MRGE
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Homework Statement


A person scuffing her feet on a wool rug on a dry day accumulates a net charge of -73 µC. How many excess electrons does this person get?


Homework Equations



so i did 73x10^-6 / 1.602x10^19 and i got 4.5x10^14

but one of the questions is By how much does her mass increase?

The Attempt at a Solution



I have no idea how i would go about and in finding this.
 
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  • #2
One has the number of electrons. Now what is the rest mass of an electron? Use the two numbers to determine the total mass of electrons gained.
 
  • #3


I would suggest approaching this problem by considering the mass of an individual electron and the overall charge of the person. The mass of an electron is approximately 9.11 x 10^-31 kilograms. Since the person has a net charge of -73 µC, this means they have gained 73 x 10^-6 Coulombs of negative charge. Using the equation Q = ne, where Q is the charge, n is the number of excess electrons, and e is the charge of a single electron, we can rearrange to solve for n. This gives us n = Q/e, which in this case is (73 x 10^-6 C) / (1.602 x 10^-19 C) = 4.5 x 10^14 excess electrons.

To calculate the mass increase, we can multiply the number of excess electrons by the mass of a single electron. This gives us (4.5 x 10^14 electrons) x (9.11 x 10^-31 kg/electron) = 4.1 x 10^-16 kg. Therefore, the person's mass would increase by approximately 4.1 x 10^-16 kg.

It is important to note that this calculation assumes that all excess electrons are confined to the person's body and do not escape into the surrounding environment. Additionally, the mass increase is incredibly small and would likely not be noticeable on a person's scale.
 

1. What is the relationship between gaining electrons and mass?

When an atom gains electrons, its mass increases. This is because electrons have a very small mass, but when added to an atom, they contribute to the overall mass of the atom.

2. How does gaining electrons affect the mass of an atom?

Gaining electrons causes the mass of an atom to increase. This is because electrons have a very small mass, but when added to an atom, they contribute to the overall mass of the atom.

3. Is there a specific formula for finding the mass after gaining electrons?

Yes, the formula for finding the mass after gaining electrons is: final mass = initial mass + number of electrons x mass of one electron.

4. Can an atom gain an unlimited number of electrons?

No, an atom can only gain a certain number of electrons before it becomes unstable. The number of electrons an atom can gain depends on its atomic structure and the number of valence electrons it has.

5. How does the mass of an atom change after gaining electrons in a chemical reaction?

The mass of an atom will increase after gaining electrons in a chemical reaction. This increase in mass can be calculated using the formula: final mass = initial mass + number of electrons x mass of one electron.

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