Question

Total charge on \[75\,{\text{kg}}\] electrons is - - - C.
(Mass of electron, \[{m_e} = 9 \times {10^{ - 31}}\,{\text{kg}}\])
A. \[ - 1.25 \times {10^{13}}\]
B. \[ - 6.25 \times {10^{18}}\]
C. \[ - 1.33 \times {10^{13}}\]
D. \[ - 1.6 \times {10^{19}}\]

Answer 1

Hint: Using the total mass of the electrons and mass of a single electron, determine the number of electrons present in the given mass of electrons. Then multiply these total number of electrons by the charge on a single electron to determine the total charge on 75 kg of electrons.

Complete step by step answer:
We have given the total mass of electrons is \[75\,{\text{kg}}\].
\[m = 75\,{\text{kg}}\]
The mass of a single electron is \[9 \times {10^{ - 31}}\,{\text{kg}}\].
\[{m_e} = 9 \times {10^{ - 31}}\,{\text{kg}}\]
Let us determine the number of electrons in the given mass of the electrons.
The number \[n\] of electrons in the given mass is given by the ratio of total mass of the electrons and
the mass of a single electron.
\[n = \dfrac{m}{{{m_e}}}\]
Substitute \[75\,{\text{kg}}\] for \[m\] and \[9 \times {10^{ - 31}}\,{\text{kg}}\] for \[{m_e}\] in the above equation.
\[n = \dfrac{{75\,{\text{kg}}}}{{9 \times {{10}^{ - 31}}\,{\text{kg}}}}\]
\[ \Rightarrow n = 8.33 \times {10^{31}}\]
Hence, the number of electrons in 75 kg of electrons is \[8.33 \times {10^{31}}\].
The charge \[{q_e}\] on a single electron is \[ - 1.6 \times {10^{ - 19}}\,{\text{C}}\].
\[{q_e} = - 1.6 \times {10^{ - 19}}\,{\text{C}}\]
Let us now determine the total charge on \[n\] number of electrons.
The total charge \[q\] on \[n\] number of electrons is the product of the number of electrons and the charge on a single electron.
\[q = n{q_e}\]
Substitute \[8.33 \times {10^{31}}\] for \[n\] and \[1.6 \times {10^{ - 19}}\,{\text{C}}\] for \[{q_e}\] in the above equation.
\[q = \left( {8.33 \times {{10}^{31}}} \right)\left( { - 1.6 \times {{10}^{ - 19}}\,{\text{C}}} \right)\]
\[ \Rightarrow q = - 13.3 \times {10^{12}}\,{\text{C}}\]
\[ \Rightarrow q = - 1.33 \times {10^{13}}\,{\text{C}}\]
Therefore, the total charge on 75 kg of electrons is \[ - 1.33 \times {10^{13}}\,{\text{C}}\].

So, the correct answer is “Option C”.

Note:
The students may forget to determine the total number of electrons in the given mass of the electrons and directly multiply the mass by the charge on a single electron. But the answer found in this way is not correct. Since the electrons possess negative charge, the students should not forget to take the negative sign with the charge of the electron.