Finding the mass after gaining elctrons

[MRGE]

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.

 

[Astronuc]

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.

 

[nlightner]

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.