Polythene Charge Transfer Problem

When a piece of polythene is rubbed with wool, a charge of \( -2 \times 10^{-7} \, \text{C} \) is developed on the polythene. What is the amount of mass transferred to the polythene?

Select the Correct Option

A) \( 1.14 \times 10^{-17} \, \text{kg} \)

B) \( 2.28 \times 10^{-18} \, \text{kg} \)

C) \( 1.14 \times 10^{-18} \, \text{kg} \)

D) \( 2.28 \times 10^{-17} \, \text{kg} \)

Explanation

When the polythene develops a charge of \( -2 \times 10^{-7} \, \text{C} \), the number of electrons transferred (ignoring the sign, since mass is positive) is given by:

\( n = \frac{|\text{Charge}|}{e} = \frac{2 \times 10^{-7}}{1.6 \times 10^{-19}} \approx 1.25 \times 10^{12} \, \text{electrons} \)

The mass of one electron is approximately \( 9.11 \times 10^{-31} \, \text{kg} \). Therefore, the total mass transferred is:

\( m = n \times m_e \approx 1.25 \times 10^{12} \times 9.11 \times 10^{-31} \, \text{kg} \approx 1.14 \times 10^{-18} \, \text{kg} \)

Hence, the correct answer is option C.