What is the amount of charge possessed by `1 kg` of electrons

Options

A. `1.76xx10^(11)C`
B. `1.76xx10^(-9)` C
C. `1.76xx10^(-7)C`
D. `1.76xx10^(-5)` C

Answer

To find the amount of charge possessed by 1 kg of electrons, we can follow these steps:

### Step 1: Determine the charge of a single electron.
The charge of one electron is approximately:
\[ e = 1.6 \times 10^{-19} \text{ coulombs} \]

### Step 2: Determine the mass of a single electron.
The mass of one electron is approximately:
\[ m_e = 9.1 \times 10^{-31} \text{ kg} \]

### Step 3: Calculate the number of electrons in 1 kg.
To find the number of electrons in 1 kg, we can use the formula:
\[ \text{Number of electrons} = \frac{\text{Total mass}}{\text{Mass of one electron}} = \frac{1 \text{ kg}}{9.1 \times 10^{-31} \text{ kg}} \]
Calculating this gives:
\[ \text{Number of electrons} \approx \frac{1}{9.1 \times 10^{-31}} \approx 1.1 \times 10^{30} \]

### Step 4: Calculate the total charge of 1 kg of electrons.
The total charge can be calculated by multiplying the number of electrons by the charge of one electron:
\[ \text{Total charge} = \text{Number of electrons} \times \text{Charge of one electron} \]
Substituting the values we have:
\[ \text{Total charge} = (1.1 \times 10^{30}) \times (1.6 \times 10^{-19} \text{ C}) \]
Calculating this gives:
\[ \text{Total charge} \approx 1.76 \times 10^{11} \text{ C} \]

### Conclusion:
Thus, the amount of charge possessed by 1 kg of electrons is approximately:
\[ \text{Total charge} \approx 1.76 \times 10^{11} \text{ coulombs} \]