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

In order to solve this question, the concept of quantization of charge is important. It says that charge on a surface can be counted in the number of electrons and protons. Here, with the help of that number of electrons can be calculated. This number would help in the calculation of transfer of charges. The one solving this question should know the charge and mass of the electron.

Complete step by step answer:
It is given in the question that the negative charge on the polythene piece is $q = 3 \times {10^{ - 7}}C$ .
As we know that the charge on an electron is equal to, $e = 1.6 \times {10^{ - 19}}C$ .
(A) For the number of the electrons, As we know the law of quantization of charges which can be described the equation form below as,
$q = ne$
We have to find $n$ that is the number of electrons, is so putting $n$ on one side and putting all the other things on other side we have,
$n = \dfrac{q}{e}$
Putting the values of $q$ and $e$ we have,
$n = \dfrac{{3 \times {{10}^{ - 7}}C}}{{1.6 \times {{10}^{ - 19}}C}}$
On solving we get,
$n = 1.875 \times {10^{12}}$

So, we have the number of electrons transferred as $n = 1.875 \times {10^{12}}$.

(B) Yes, there is a transfer of mass from wool to polythene.
As we know that mass of an electron is equal to, $m = 9.1 \times {10^{ - 31}}kg$
Here, the transfer of mass would be given by formula,
$M = nm$
Putting the values of $m$ and $n$ we have,
$M = 1.875 \times {10^{12}} \times 9.1 \times {10^{ - 31}}kg$
On simplifying we get,
$M = 17.0 \times {10^{ - 19}}kg$

Hence, the mass transferred from wool to polythene is given by $M = 17.0 \times {10^{ - 19}}kg$.

Note: Quantization of charge means that charge can assume only certain discrete values. That is to say the observed value of electric charge $q$ of a particle will be integral multiples of $e$ that is the charge on an electron. This can be represented as $q = ne$, here $n$ can be both positive and negative integers.