Question

What is the number of electrons that would weigh 1 kg? Mass of an electron is \[9.11 \times {10^{( - 31)}}kg\].

Answer 1

Hint: The mass of the electron is provided, and the mass which the electrons need to achieve is 1 kilogram. Thus we will use this and multiply the number of electrons with the mass of a single electron to find out the total mass which those particular numbers of electrons are able to achieve which should be equal to 1 kilogram.

Complete step by step answer:
Mass is an intrinsic property, which is a quantitative measure of inertia and is a fundamental property of all kinds of matter or quantity. Mass is measured in a number of units such as gram, kilogram, ton, tone, milligram and many more. Electrons are fundamental particles. It possesses a charge and charge is also a fundamental property of matter as well. Now we are given that the mass of the electron is equal to \[9.11 \times {10^{( - 31)}}kg\].

We want to find the number of electrons which are needed to form a mass which is equivalent to 1 kilogram. Thus we will use the below formula to find the number of electrons.
\[M = n{m_e}\]
Here, M is the total mass which is given, n is the number of electrons which are present and \[{m_e}\] is the mass of a single electron which is present. Thus, using the given numbers in the question in the given formula, we will have;
\[
1kg=n\centerdot 9.11\times {{10}^{(-31)}}kg \\
\Rightarrow n=\dfrac{1}{9.11\times {{10}^{(-31)}}} \\
\therefore n=1.097\times {{10}^{(32)}} \\
\]
Thus, the number of electrons which are needed to form 1 kilogram of mass is \[1.097 \times {10^{(32)}}\].

Note:According to the conservation of mass, mass is a fundamental property which can neither be created nor can it be destroyed. The total mass of a system has to be constant. Although, according to modern physics, mass can be converted into energy according to Einstein's famous equation\[E = m{c^2}\].