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

Options

A. `6.25xx10^(10)C`
B. `1.76xx10^(11)C`
C. `1.76xx10^(10)C`
D. `1.25xx10^(10)C`

Explanation

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

### Step 1: Determine the mass of a single electron
The mass of one electron is given as:
\[ m_e = 9.1 \times 10^{-31} \text{ kg} \]

### Step 2: Calculate the number of electrons in 1 kg
To find the number of electrons in 1 kg, we divide the total mass (1 kg) by the mass of a single electron:
\[ N = \frac{1 \text{ kg}}{m_e} = \frac{1 \text{ kg}}{9.1 \times 10^{-31} \text{ kg}} \]

Calculating this gives:
\[ N \approx 1.1 \times 10^{30} \text{ electrons} \]

### Step 3: Determine the charge of a single electron
The charge of one electron is given as:
\[ q_e = -1.6 \times 10^{-19} \text{ C} \]

### Step 4: Calculate the total charge of 1 kg of electrons
The total charge \( Q \) possessed by 1 kg of electrons can be calculated by multiplying the number of electrons by the charge of a single electron:
\[ Q = N \times q_e \]
\[ Q = (1.1 \times 10^{30}) \times (-1.6 \times 10^{-19}) \]

Calculating this gives:
\[ Q \approx -1.76 \times 10^{11} \text{ C} \]

### Step 5: Final result
The total charge possessed by 1 kg of electrons is approximately:
\[ Q \approx -1.76 \times 10^{11} \text{ C} \]