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: Determine the mass of one electron
The mass of one electron is given as:
\[ \text{Mass of one electron} = 9.1 \times 10^{-31} \text{ kg} \]

### Step 2: Convert the mass of one electron to grams
Since we need the mass in grams, we convert kilograms to grams by multiplying by 1000 (since 1 kg = 1000 g):
\[ \text{Mass of one electron in grams} = 9.1 \times 10^{-31} \text{ kg} \times 1000 \text{ g/kg} = 9.1 \times 10^{-28} \text{ g} \]

### Step 3: Calculate the number of electrons in 1 gram
To find the number of electrons that weigh 1 gram, we can use the formula:
\[ \text{Number of electrons} = \frac{\text{Total mass}}{\text{Mass of one electron}} \]
Substituting the values:
\[ \text{Number of electrons} = \frac{1 \text{ g}}{9.1 \times 10^{-28} \text{ g}} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ \text{Number of electrons} = \frac{1}{9.1 \times 10^{-28}} \approx 1.098 \times 10^{27} \]

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

### Final Answer
The correct option is:
**Option 1: \( 1.098 \times 10^{27} \) electrons.**

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