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Chapter 11: Problem 1520

When a Piece of Polythene is rubbed with wool, a charge of \(-2 \times 10^{-7}\) is developed on polythene. The mass transferred to polythene is $\ldots \mathrm{kg}$. (A) \(11.38 \times 10^{-19}\) (B) \(5.69 \times 10^{-19}\) (C) \(2.25 \times 10^{-19}\) (D) \(9.63 \times 10^{-19}\)

Short Answer

Expert verified
The mass transferred to polythene is (A) \(1.138 \times 10^{-18}\ \mathrm{kg}\).

Step by step solution

01

Calculate the number of electrons transferred

We know that the charge of a single electron is approximately \(e = -1.6 \times 10^{-19} \mathrm{C}\). We're given that the charge developed on polythene is \(Q = -2 \times 10^{-7} \mathrm{C}\). To find the number of electrons transferred, we can use the formula: Number of electrons transferred = \(\frac{\text{Total Charge}}{\text{Charge of one electron}}\)
02

Calculate the mass transferred

First, find the number of electrons transferred by dividing the total charge (Q) by the charge of one electron (e): Number of electrons transferred = \(\frac{-2 \times 10^{-7}}{-1.6 \times 10^{-19}}\) Number of electrons transferred = \(1.25 \times 10^{12}\) Now, we need to find the mass of electrons transferred. We know that the mass of a single electron is approximately \(m_e = 9.1 \times 10^{-31} \mathrm{kg}\). To find the mass transferred, we can multiply the number of electrons transferred by the mass of a single electron: Mass transferred = Number of electrons transferred \(\times\) Mass of one electron
03

Calculate the mass transferred

Calculate the mass transferred by multiplying the number of electrons transferred by the mass of one electron: Mass transferred = \(1.25 \times 10^{12} \times 9.1 \times 10^{-31}\) Mass transferred = \(1.1375 \times 10^{-18}\) Finally, we can compare our result with the given options: (A) \(11.38 \times 10^{-19} \approx 1.138 \times 10^{-18}\) (correct) (B) \(5.69 \times 10^{-19}\) (C) \(2.25 \times 10^{-19}\) (D) \(9.63 \times 10^{-19}\) The correct answer is (A) \(1.138 \times 10^{-18}\ \mathrm{kg}\).

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