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Question: When \({{10}^{19}}\) electrons are removed from a neutral metal plate through some process, the char...

When 1019{{10}^{19}} electrons are removed from a neutral metal plate through some process, the charge on it becomes_____________
A. -1.6C
B. +1.6C
C. 1019C{{10}^{19}}C
D. 10−19C{{10}^{-19}}C

Explanation

Solution

As a first step you could recall the property of quantization of charge and thus determine the charge that is being removed from the metal plate along with the 1019{{10}^{19}} electrons. Now remember the law of conservation of charge in an isolated system. Now you could easily get the charge developed on the plate as the result of removal of the given number of electrons.
Formula used:
Quantization of charge,
q=±neq=\pm ne

Complete step by step answer:
In the question we are given a situation we are removing 109{{10}^{9}} electrons from a neutral metal plate through some unknown process. We are asked to find the charge that remains on the metal plate that will be no more neutral after the removal of that many electrons from it.
We know that electric charge of an electron is given by,
e=1.6×10−19Ce=1.6\times {{10}^{-19}}C
We also know that one among the basic properties of charges is the quantization of charges. By this property, all free charges are integral multiples of a basic unit of charge that is denoted by ‘e’ which is the charge of an electron. Mathematically we could express this property as,
q=±neq=\pm ne
So we are removing 1019{{10}^{19}} electrons from the neutral plate, that is,
n=1019n={{10}^{19}}
The charge q carried by these 1019{{10}^{19}} electrons will be,
q=−(1019×1.6×10−19)q=-\left( {{10}^{19}}\times 1.6\times {{10}^{-19}} \right)
⇒q=−1.6C\Rightarrow q=-1.6C
So we see that -1.6C of charge is being removed from the neutral metal plate.
Let us recall another basic property of electric charge that is the conservation of electric charge which states that charges can neither be created nor destroyed. So an opposite charge of equal magnitude as that of the removed electrons should be developed in the metal plate for the charge to be conserved in this process.
So the charge on the metal plate after the removal of the electrons will be +1.6C.

Hence, the answer to the question is option B.

Note:
The magnitude of the basic unit of charge ‘e’ does not just represent the charge of an electron but also that of proton. But by convention we take the charge of an electron negative and that of protons positive. We have used this convention to find the above answer. Also, both the basic properties of an electric charge used in this question are experimentally proven.