The number of electrons which will together weigh one gram is:
A. \[1.098\times {{10}^{27}}\] electrons
B. \[9.1096\times {{10}^{31}}\] electrons
C. 1 electron
D. \[1\times {{10}^{4}}\] electrons

Hint: To calculate the number of electrons in 1 g weight, we should know the mass of the electron.
We have to use an electric field perpendicular to the magnetic field in order to measure the mass of an electron.
Mass of the electron is \[9.1096\times {{10}^{-31}}\]kg.
Keep it in mind that the mass of the electron is not equal to charge of the electron.
1 kg is equal to 1000 g
1 g is equal to 1000 mg

Complete step by step answer:
In the question it is given that weight w is 1 g
We know that the mass of one electron is \[9.1096\times {{10}^{-31}}\]kg
We have to convert mass of electron in to grams = \[9.1096\times {{10}^{-31}}\times 1000g\]
                                                            = \[9.1096\times {{10}^{-28}}g\]
so, the number of electrons in 1 g =\[\dfrac{1}{9.1\times {{10}^{-28}}}\]
                        = \[1.098\times {{10}^{27}}\]electrons
Therefore the number of electrons in 1 g = \[1.098\times {{10}^{27}}\]electrons.
Coming to the given options, Option B, \[9.1096\times {{10}^{31}}\]electrons, it is wrong because this value is too high.
Coming to option C, 1 electron. It is also wrong because 1 g weight is not equal to 1 electron.
Coming to option D, \[1\times {{10}^{4}}\]electrons, it is also wrong because the value is too less than the value obtained from the above calculation.
Coming to option A, \[1.098\times {{10}^{27}}\]electrons. It is correct because it is matching with the calculated answer.
So, the correct option is A.

Note: Don’t be confused with the words, mass of the electron and charge of the electron. Both are not the same.
Mass of the electron = \[9.1096\times {{10}^{-31}}\]kg.
Charge of the electron = \[1.602\times {{10}^{-19}}\] coulombs (C)