A polythene piece rubbed with wool is found to have negative charge of `3.6xx10^(-7)C`. Calculate the number of electrons transferred from wool to polythene. If an electron has a mass `9.1 xx 10^(-31) kg`, find the mass transferred to polythene.

Options

A. `2.25xx10^(10) kg`
B. `6.25xx10^(-18) kg`
C. `2.05xx10^(-18) kg`
D. `4.15xx10^(-18) kg`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the charge of an electron
The charge of a single electron is known to be:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]

### Step 2: Use the formula for total charge
We know that the total charge transferred (Q) is given as:
\[ Q = 3.6 \times 10^{-7} \, \text{C} \]

If \( n \) is the number of electrons transferred, then the total charge can also be expressed as:
\[ Q = n \cdot e \]

### Step 3: Rearranging the formula to find the number of electrons
We can rearrange the formula to find \( n \):
\[ n = \frac{Q}{e} \]

### Step 4: Substitute the values into the equation
Substituting the known values:
\[ n = \frac{3.6 \times 10^{-7} \, \text{C}}{1.6 \times 10^{-19} \, \text{C}} \]

### Step 5: Calculate the number of electrons
Now, performing the calculation:
\[ n = \frac{3.6}{1.6} \times 10^{-7 + 19} \]
\[ n = 2.25 \times 10^{12} \]

So, the number of electrons transferred is:
\[ n = 2.25 \times 10^{12} \]

### Step 6: Calculate the mass transferred to polythene
To find the mass transferred, we use the mass of a single electron:
\[ m_e = 9.1 \times 10^{-31} \, \text{kg} \]

The total mass \( m \) transferred can be calculated as:
\[ m = n \cdot m_e \]

### Step 7: Substitute the values into the equation
Substituting the values we found:
\[ m = 2.25 \times 10^{12} \cdot 9.1 \times 10^{-31} \]

### Step 8: Calculate the total mass
Now, performing the calculation:
\[ m = 2.25 \times 9.1 \times 10^{12 - 31} \]
\[ m = 20.475 \times 10^{-19} \, \text{kg} \]

### Step 9: Express the mass in scientific notation
Converting this to proper scientific notation:
\[ m = 2.0475 \times 10^{-18} \, \text{kg} \]

### Final Answers
1. The number of electrons transferred is \( 2.25 \times 10^{12} \).
2. The mass transferred to polythene is approximately \( 2.05 \times 10^{-18} \, \text{kg} \).

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