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How many electrons are present in a particle which carries a charge of $5.5 \times {10^{ - 16}}C$?
A. 3432
B. 1560
C. 8240
D. 2432

Last updated date: 20th Jun 2024
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Hint: The electron is a subatomic particle present in an atom along with other subatomic particles such as protons and neutrons. The total number of electrons and protons in an atom determines the net charge of an atom. The elementary charge of an electron has an approximate value of $1.6022 \times {10^{ - 19}}C$. The elementary charge here refers to the electric charge carried by a single electron. It is denoted as –e for an electron.

Formula used: The formula we will be using to calculate the number of electrons present in the particle is:
$n = \dfrac{q}{e}$
The letter ‘n’ denotes the number of electrons present in the particle carrying charge of the magnitude of $5.5 \times {10^{ - 16}}C$. The C here is the charge of the particle of which number of electrons we have to find and e is the elementary charge of an electron.

Complete step by step answer:
The charge is also referred to as the electric charge, electrical charge or electrostatic charge. It is denoted by the symbol q. The charge is expressed as the extent to which a particle has more or less electrons than protons with positive charge. The SI unit of charge is coulomb or C. Charge is said to be quantized, that is charge is expressed in the multiple of charge on an electron or a proton.
As we know, the charge is quantized and this can be expressed as:
$q = n \times e$………… (1)
As we know, q is the symbol used for expressing charge in coulombs, n is the number of electrons present in the particle and it can be positive or negative value. The elementary charge equals to $1.6022 \times {10^{ - 19}}C$.
To obtain the number of electrons present in particle we need to rearrange formula (1)
On rearranging the formula (1), we get,
$n = \dfrac{q}{e}$……………….. (2)
We will now substitute the respective values in formula (2) to find out the number of electrons in the said particle.
Let us first write down the given values.
$q = 5.5 \times {10^{ - 16}}C$
$e = 1.6022 \times {10^{ - 19}}C$
On putting respective values in formula (2), we get,
$n = \dfrac{{5.5 \times {{10}^{ - 19}}C}}{{1.6022 \times {{10}^{ - 16}}C}}$
$\therefore n = 3432electrons$
The number of electrons present in a particle carrying charge of $5.5 \times {10^{ - 16}}C$ is 3432.

So, the correct answer is A.

Additional information:
The symbol used for denoting elementary charge is e and in order to avoid confusion, e is taken as the sign for positive elementary charge that is charged on a single proton. The electrons will have a negative value of e. The electrons and other freely existing charged subatomic particles discovered till now possess an electric charge equivalent to that of elementary charge.

Note: We are aware of the fact that charge of a particle is the measure of imbalance between the number of protons and electrons present in that particle. This is helpful in determining the total charge on a positively and negatively charged object. To find out the net charge on a positively charged object or object containing excess protons, you need to subtract the total number of electrons in that particle from the total number of protons in that object. This will provide us the number of excess protons. This number of excess protons when multiplied by the value of elementary charge, will give us the value of total charge on that object.