Question

A polythene piece rubbed with wool is found to have a negative charge of $3\times {{10}^{-7}}C~$ .
(a) Estimate the number of electrons transferred (from which to which?)
(b) Is there a transfer of mass from wool to polythene?

Answer 1

We must know that if there is an excess of electrons in a body, the charge on that body will be negative whereas if there is a deficiency of electrons, the charge on that particular body will be positive. We should be aware that as electrons are also a part of matter, they also have well defined mass. Hence, whenever there is a transfer of charge, mass also gets exchanged. But this change in mass is negligible so one can proceed without considering the loss.

Formula used:
Formula used:
$q=ne$
Where, $q$ is the charge transferred when $n$ number of electrons carrying charge $e$ on each is exchanged.

Complete step by step answer:
In the question, it is given that the charge is transferred such that the polythene piece gets a negative charge of $3\times {{10}^{-7}}C$ . This means polythene has an excess of electrons. Hence electrons must be transferred from wool to polythene.
(a) To find the number of electrons transferred, we need to put the value of charge of one electron in the equation $q=ne$ , we get;
$\begin{aligned} & 3\times {{10}^{-7}}C=n\times \left( 1.6\times {{10}^{-19}} \right) \\\ & \Rightarrow n=\dfrac{3\times {{10}^{-7}}C}{1.6\times {{10}^{-19}}C}=1.875\times {{10}^{12}} \\\ \end{aligned}$
So, a total of $1.875\times {{10}^{12}}$ electrons are transferred from wool to polythene.
(b) To find the mass of an electron transferred from wool to polythene, we must know the mass of one electron. i.e. ${{m}_{e}}=9.1\times {{10}^{-31}}kg$
Hence,

& \text{total mass of n electrons }=n\times {{m}_{e}} \\\ & \Rightarrow ~n\times {{m}_{e}}=1.875\times {{10}^{12}}\times 9.1\times {{10}^{-31}}=1.707\times {{10}^{-18}}kg \\\ \end{aligned}$$ So, a total of $$1.707\times {{10}^{-18}}kg$$ of mass is transferred from wool to polythene. **Note:** We can see that mass transferred is very negligible, hence it could be neglected. It’s important to realize that if a negative charge is in excess, it means some electrons must be transferred from some other body. But if we say that positive charge in excess, it doesn’t imply that protons are transferred. In fact, protons don’t move at all. They are just present inside the nucleus. Rather positive charge means a deficiency of electrons.