Question

Among the following, the charge that does not exist on any type of charged body is:

• A. \( 3.2 \times 10^{-19} \, \text{C} \)
• B. \( 6.4 \times 10^{-19} \, \text{C} \)
• C. \( 9.6 \times 10^{-20} \, \text{C} \)
• D. \( 9.6 \times 10^{-18} \, \text{C} \)

Hint:

The charge on any charged body must be a multiple of the fundamental charge, which is \( e = 1.6 \times 10^{-19} \, \text{C} \).

Answer 1

The Correct Option is C

Step 1: Understand the concept of quantization of charge.
Charge on any object must be an integral multiple of elementary charge: \[ q = n \cdot e, \quad \text{where } e = 1.6 \times 10^{-19} \, \text{C},\quad n \in \mathbb{Z} \]
Step 2: Check divisibility of each given charge by \( e \). \begin{itemize} \item Option (1): \( 3.2 \times 10^{-19} = 2 \cdot e \) → valid. \item Option (2): \( 6.4 \times 10^{-19} = 4 \cdot e \) → valid. \item Option (3): \( 9.6 \times 10^{-20} \div 1.6 \times 10^{-19} = 0.6 \) → not an integer → not valid. \item Option (4): \( 9.6 \times 10^{-18} \div 1.6 \times 10^{-19} = 60 \) → valid. \end{itemize} So, the charge in option (3) is not a multiple of the elementary charge and hence cannot exist on any charged body.