Question

Which of the following charge is not possible on a body?

(1) 1.6 x ${10}^{-18}$ C

(2) 1.6 x ${10}^{-20}$ C

(3) 1.6 x ${10}^{-14}$ C

(4) 1.6 x ${10}^{-5}$ C

Answer 1

Explanation of correct option:

Option 2)

1. According to the quantisation of charge, the charge on any body is always an integral multiple of the charge possessed by an electron.
2. That is, ​if $q$ be the charge on a body then, it can be represented as $q=ne$ , here, n is an integer and e is the charge on an electron which is equal to $1.6\times {10}^{-19}C$ .
3. It is not possible for any body to have a charge which is a fractional multiple of e.
4. As,

   $=1.6\times {10}^{-20}C$

   $=1.6\times {10}^{-19}\times {10}^{-1}C$

   $=\frac{1}{10}eC$

   Which is a fractional multiple of e therefore it is not a possible value of charge possessed by a body.

Explanation of incorrect options:

Option 1)

$1.6\times {10}^{-18}C=1.6\times {10}^{-18}\times \frac{10}{10}C$

$=10\times 1.6\times {10}^{-18}\times {10}^{-1}C$

$=10\times (1.6\times {10}^{-19}C)$

$=10\times e$ where 10 is an integer.

Thus,

It is clear that$1.6\times {10}^{-18}C$ is a possible value of charge on a body as it is an integral multiple of the charge e.

Option 3)

$1.6\times {10}^{-14}C=1.6\times {10}^{-14}\times \frac{{10}^5}{{10}^5}C$

$={10}^5\times 1.6\times {10}^{-19}C$

$={10}^5(1.6\times {10}^{-19}C)$

$={10}^{5}e$, where ${10}^5$ is also an integer.

Thus, it is clear that $1.6\times {10}^{-14}C$ is a possible value of charge on a body as it is an integral multiple of the charge e.

Option 4)

$1.6\times {10}^{-5}C=1.6\times {10}^{-5}\times \frac{{10}^{14}}{{10}^{14}}C$

$={10}^{14}\times 1.6\times {10}^{-19}C$

$={10}^{14}(1.6\times {10}^{-19}C)$

$={10}^{14}e$, where ${10}^{14}$ is also an integer.

Thus, it is clear that $1.6\times {10}^{-5}C$ is a possible value of charge on a body as it is an integral multiple of the charge e.

Hence,

Option 2) $1.6\times {10}^{-20}C$ is the correct option.