The number of electrons which will together weigh one gram is

Options

A. `1.098xx10^(27)` electrons
B. `9.1096xx10^(31)` electrons
C. 1 electron
D. `1xx10^(4)` electrons

Explanation

To find the number of electrons that together weigh one gram, we can follow these steps:

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

### Step 2: Convert the total weight from grams to kilograms
Since the weight given is in grams, we need to convert it to kilograms. We know that:
\[ 1 \text{ gram} = 10^{-3} \text{ kg} \]
Thus, the total weight in kilograms is:
\[ \text{Total weight} = 1 \text{ gram} = 10^{-3} \text{ kg} \]

### Step 3: Calculate the number of electrons
To find the number of electrons (\(n\)) that together weigh one gram, we can use the formula:
\[ n = \frac{\text{Total weight}}{\text{Mass of one electron}} = \frac{10^{-3} \text{ kg}}{9.1 \times 10^{-31} \text{ kg}} \]

### Step 4: Perform the division
Calculating the division:
\[ n = \frac{10^{-3}}{9.1 \times 10^{-31}} = \frac{1}{9.1} \times 10^{28} \]
Calculating \( \frac{1}{9.1} \):
\[ \frac{1}{9.1} \approx 0.1098 \]
Thus,
\[ n \approx 0.1098 \times 10^{28} \]

### Step 5: Adjust the scientific notation
To express this in standard scientific notation:
\[ n \approx 1.098 \times 10^{27} \]

### Conclusion
Therefore, the number of electrons that together weigh one gram is approximately:
\[ \boxed{1.098 \times 10^{27}} \text{ electrons} \]