Question

The specific charge of electrons is less than the specific charge of protons.
A.True
B.False

Answer 1

Hint: Specific charge of a body or a particle can be explained as the ratio of the charge of the body to the mass of the body. This can be mathematically represented as:
Formula Used:
 Specific charge \[ = \dfrac{{ch\arg e\,\,of\,\,particle}}{{mass\,\,of\,\,particle}}\]

Complete step by step answer:
Before we move forward with the solution of the given question, let us first understand some important basic concepts.
The masses and charge of both a proton and an electron are fixed. The mass of an electron is equal to \[9.1 \times {10^{ - 31}}\] kg, while the charge on an electron is equivalent to \[ - 1.6 \times {10^{ - 19}}\] C. On the other hand, the mass of a proton is equal to \[1.67 \times {10^{ - 27}}\] kg and the charge on a proton is equivalent in magnitude but opposite to the sign of the charge on an electron. Hence, the charge on a proton is \[1.6 \times {10^{ - 19}}\] C.
We can observe that there is a large difference in the masses of a proton and an electron. To be more specific, the mass of a proton is equal to about 1836 times the mass of an electron. On the other hand, the magnitude of the charge on both these particles is equal. Hence, the specific charge on both these particles can be calculated as:
Specific charge of electron \[ = \dfrac{{ - 1.6 \times {{10}^{ - 19}}}}{{9.1 \times {{10}^{ - 31}}}} = - 1.759 \times {10^{11}}\] C/kg
Specific charge of proton \[ = \dfrac{{1.6 \times {{10}^{ - 19}}}}{{1.67 \times {{10}^{ - 27}}}} = 9.58 \times {10^7}\] C/kg
Hence, we can see that the magnitude of the specific charge of an electron is greater than the specific charge of a proton.
Hence, the given statement is false.

Hence, Option B is the correct option.

Note:
An electron has the greatest specific charge of any particle. To beat it you would either need more charge for the same mass or else a lower mass and the same charge. As of now, we have not been able to find such a particle.