Question

What is the e/m value of an electron?
\[{\text{A}}{\text{. }}1.6 \times {10^{ 11}}\] C/kg
\[{\text{B}}{\text{. }}1.6 \times {10^{ - 19}}\] C/kg
\[{\text{C}}{\text{. }}1.759 \times {10^{11}}\] C/kg
\[{\text{D}}{\text{. 901}} \times {10^{ - 31}}\] C/kg

Answer 1

Hint: Here, we will proceed by defining the term electron. Then, we will discuss the mass comparison of electrons with that of an atom. Finally, we will divide the value of the charge to that of the mass of any electron.

Complete step-by-step answer:

Electron, which is the lightest known stable subatomic particle. It has a negative charge against it.

${\left( {\dfrac{1}{{1836}}} \right)^{{\text{th}}}}$ mass of the mass of a proton gives the rest mass of an electron. Therefore, an electron is considered almost massless compared to a proton or a neutron, and the mass of an electron is not included in the measurement of an atom's mass number.

Through electrical conductors, the current flow is the outcome of transferring electrons independently from atom to atom, and usually from negative to positive electric poles. Current also happens in semiconductor materials as a movement of electrons. Within a semiconductor an electron deficient atom is considered a hole. Holes "jump" usually from the positive to the negative electric poles.

As we know that the charge on any electron is $1.6 \times {10^{ - 19}}$ coulomb i.e., e = $1.6 \times {10^{ - 19}}$ C

Also the mass of an electron is $9.1 \times {10^{ - 31}}$ kg i.e., m = $9.1 \times {10^{ - 31}}$ kg

The charge to mass ratio can be easily obtained by dividing the value of the charge on any electron by the mass of any electron

$
  \dfrac{{\text{e}}}{{\text{m}}} = \dfrac{{1.6 \times {{10}^{ - 19}}}}{{9.1 \times {{10}^{ - 31}}}} \\
   \Rightarrow \dfrac{{\text{e}}}{{\text{m}}} = \dfrac{{1.6}}{{9.1}} \times {10^{ - 19}} \times {10^{31}} \\
   \Rightarrow \dfrac{{\text{e}}}{{\text{m}}} = 0.1759 \times {10^{ - 19 + 31}} \\
   \Rightarrow \dfrac{{\text{e}}}{{\text{m}}} = 0.1759 \times {10^{12}} \\
   \Rightarrow \dfrac{{\text{e}}}{{\text{m}}} = 1.759 \times {10^{11}} \\
 $

Therefore, the value of the charge to mass ratio for any electron (i.e., e/m) is $1.759 \times {10^{11}}$ C/kg

Hence, option C is correct.

Note: In this particular problem, while finding the value of e/m we have neglected the negative sign corresponding to the charge of an electron (i.e., we are just considering the magnitude of the charge of an electron). Any atom consists of three particles including electrons, protons and neutrons.