What is charge on 90 kg of electrons?

Options

A. `1.58 '10^(13)`
B. `2.3 *10^(12)`
C. `2.53 * '10^(12)`
D. None of these

Explanation

To find the total charge on 90 kg of electrons, we can follow these steps:

### Step 1: Identify 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 90 kg
To find the number of electrons in 90 kg, we can use the formula:
\[ N = \frac{\text{Total mass}}{\text{Mass of one electron}} \]
Substituting the values:
\[ N = \frac{90 \text{ kg}}{9.1 \times 10^{-31} \text{ kg}} \]

### Step 3: Perform the calculation
Calculating \( N \):
\[ N \approx \frac{90}{9.1 \times 10^{-31}} \approx 9.89 \times 10^{31} \text{ electrons} \]

### Step 4: Identify the charge of a single electron
The charge of one electron is given as:
\[ e = -1.6 \times 10^{-19} \text{ C} \]

### Step 5: Calculate the total charge
The total charge \( Q \) can be calculated by multiplying the number of electrons by the charge of one electron:
\[ Q = N \times e \]
Substituting the values:
\[ Q = (9.89 \times 10^{31}) \times (-1.6 \times 10^{-19}) \]

### Step 6: Perform the final calculation
Calculating \( Q \):
\[ Q \approx -1.58 \times 10^{13} \text{ C} \]

Thus, the total charge on 90 kg of electrons is approximately:
\[ Q \approx -1.58 \times 10^{13} \text{ C} \]