The total number of electron is `1. g CH_4` are :

Options

A. `N//10`
B. `N`
C. `2N`
D. `3N`

Explanation

To find the total number of electrons in 1 gram of CH₄ (methane), we can follow these steps:

### Step 1: Determine the molecular weight of CH₄
- The molecular weight of CH₄ can be calculated by adding the atomic weights of its constituent atoms:
- Carbon (C) has an atomic weight of approximately 12 g/mol.
- Hydrogen (H) has an atomic weight of approximately 1 g/mol.
- Since there are 4 hydrogen atoms in CH₄, the total weight is:
\[ \text{Molecular weight of CH₄} = 12 + (4 \times 1) = 12 + 4 = 16 \text{ g/mol} \]

### Step 2: Calculate the number of moles in 1 gram of CH₄
- To find the number of moles in 1 gram of CH₄, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molecular weight (g/mol)}} \]
- For 1 gram of CH₄:
\[ \text{Number of moles of CH₄} = \frac{1 \text{ g}}{16 \text{ g/mol}} = \frac{1}{16} \text{ moles} \]

### Step 3: Determine the number of electrons in 1 mole of CH₄
- Each molecule of CH₄ contains:
- 1 carbon atom, which has 6 electrons.
- 4 hydrogen atoms, each having 1 electron, contributing a total of 4 electrons.
- Therefore, the total number of electrons in 1 mole of CH₄ is:
\[ \text{Total electrons in 1 mole of CH₄} = 6 \text{ (from C)} + 4 \text{ (from H)} = 10 \text{ electrons} \]

### Step 4: Calculate the total number of electrons in 1 gram of CH₄
- Now, we can find the total number of electrons in the amount of CH₄ we have:
\[ \text{Total electrons in 1 gram of CH₄} = \left(\frac{1}{16} \text{ moles of CH₄}\right) \times 10 \text{ electrons/mole} = \frac{10}{16} = \frac{5}{8} \text{ moles of electrons} \]

### Step 5: Convert moles of electrons to number of electrons
- To convert moles of electrons to the actual number of electrons, we use Avogadro's number (\(6.022 \times 10^{23}\) electrons/mole):
\[ \text{Total number of electrons} = \frac{5}{8} \text{ moles} \times 6.022 \times 10^{23} \text{ electrons/mole} \]
- Calculating this gives:
\[ \text{Total number of electrons} = \frac{5 \times 6.022 \times 10^{23}}{8} \approx 3.76 \times 10^{23} \text{ electrons} \]

### Final Answer
The total number of electrons in 1 gram of CH₄ is approximately \(3.76 \times 10^{23}\) electrons.

---