The mass of one mole of electron is

Options

A. `9.1 xx 10^(-28) g`
B. `0.55 mg`
C. `9.1 xx 10^(-24)g`
D. `1.008 mg`

Explanation

To find the mass of one mole 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: Convert the mass of the electron to grams
Since we need the mass in grams, we convert kilograms to grams using the conversion factor \(1 \text{ kg} = 1000 \text{ g}\):
\[ m_e = 9.1 \times 10^{-31} \text{ kg} \times 1000 \text{ g/kg} = 9.1 \times 10^{-28} \text{ g} \]

### Step 3: Use Avogadro's number to find the mass of one mole of electrons
Avogadro's number (\(N_A\)) is:
\[ N_A = 6.022 \times 10^{23} \text{ particles/mole} \]
To find the mass of one mole of electrons, we multiply the mass of a single electron by Avogadro's number:
\[ \text{Mass of 1 mole of electrons} = m_e \times N_A \]
\[ = (9.1 \times 10^{-28} \text{ g}) \times (6.022 \times 10^{23}) \]

### Step 4: Perform the multiplication
Calculating the product:
\[ = 9.1 \times 6.022 \times 10^{-28 + 23} \]
\[ = 54.78 \times 10^{-5} \text{ g} \]

### Step 5: Convert the mass to milligrams
To convert grams to milligrams, we use the conversion \(1 \text{ g} = 1000 \text{ mg}\):
\[ 54.78 \times 10^{-5} \text{ g} = 54.78 \times 10^{-2} \text{ mg} = 0.5478 \text{ mg} \]

### Step 6: Round off the answer
Rounding off to two decimal places, we get:
\[ \approx 0.55 \text{ mg} \]

### Final Answer:
The mass of one mole of electrons is approximately \(0.55 \text{ mg}\).

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