What is the total charge on 75.0 kg of electrons ?

Explanation

To find the total charge on 75.0 kg of electrons, we can follow these steps:

### Step 1: Find the mass of a single electron
The mass of a single electron is given as:
\[ m_e = 9 \times 10^{-31} \text{ kg} \]

### Step 2: Calculate the total number of electrons in 75.0 kg
To find the total number of electrons (\( N \)), we can use the formula:
\[ N = \frac{\text{Total mass of electrons}}{\text{Mass of one electron}} \]
Substituting the values:
\[ N = \frac{75.0 \text{ kg}}{9 \times 10^{-31} \text{ kg}} \]

### Step 3: Perform the calculation for \( N \)
Calculating \( N \):
\[ N = \frac{75.0}{9 \times 10^{-31}} = \frac{75.0}{9} \times 10^{31} \]
\[ N = 8.33 \times 10^{31} \text{ electrons} \]

### Step 4: Find the charge of a single electron
The charge of a single electron (\( q_e \)) is:
\[ q_e = -1.6 \times 10^{-19} \text{ C} \]

### Step 5: Calculate the total charge of all electrons
The total charge (\( Q \)) can be calculated using:
\[ Q = N \times q_e \]
Substituting the values:
\[ Q = (8.33 \times 10^{31}) \times (-1.6 \times 10^{-19}) \]

### Step 6: Perform the calculation for \( Q \)
Calculating \( Q \):
\[ Q = -1.33 \times 10^{13} \text{ C} \]

### Final Answer
The total charge on 75.0 kg of electrons is:
\[ Q \approx -1.33 \times 10^{13} \text{ C} \]

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