Question

In Milikan's oil drop experiment, which of the following charges can exist on an oil drop?
Charge on electron e = $-1.6\times {10}^{-19}\text{C}$

• A. $2.8\times {10}^{-19}\text{C}$
• B. $3.2\times {10}^{-19}\text{C}$
• C. $8.0\times {10}^{-19}\text{C}$
• D. $11.2\times {10}^{-19}\text{C}$

Answer 1

Answer: (B), (C), (D)

$11.2\times {10}^{-19}\text{C}$

We know that the charge is quantized, i.e., $Q=ne$ where $n$ is an integer.

(a) $Q=2.8\times {10}^{-19}\text{C}$
$n=\frac{Q}{e}=\frac{2.8\times {10}^{-19}\text{C}}{1.6\times {10}^{-19}\text{C}}=1.75$
Here $n$ is a non-integer value.

(b) $Q=3.2\times {10}^{-19}\text{C}$
$n=\frac{Q}{e}=\frac{3.2\times {10}^{-19}\text{C}}{1.6\times {10}^{-19}\text{C}}=2$
Here $n$ is an integer value.

(c) $Q=8.0\times {10}^{-19}\text{C}$
$n=\frac{Q}{e}=\frac{8.0\times {10}^{-19}\text{C}}{1.6\times {10}^{-19}\text{C}}=5$
Here $n$ is an integer value.

(d) $Q=11.2\times {10}^{-19}\text{C}$
$n=\frac{Q}{e}=\frac{11.2\times {10}^{-19}\text{C}}{1.6\times {10}^{-19}\text{C}}=7$
Here $n$ is an integer value.

So option (b), (c) and (d) are correct.