If mass of an electron is `9.1xx10^(-31)` kg, the number of electrons in 1 mg is

Options

A. `1.09xx10^(27)`
B. `1.09xx10^(24)`
C. `9.1xx10^(28)`
D. `9.1xx10^(31)`

Explanation

To find the number of electrons in 1 mg, we can follow these steps:

### Step 1: Convert 1 mg to kg
1 milligram (mg) is equal to \(1 \times 10^{-3}\) grams. Since 1 gram is equal to \(1 \times 10^{-3}\) kg, we can convert milligrams to kilograms:
\[ 1 \text{ mg} = 1 \times 10^{-3} \text{ g} = 1 \times 10^{-6} \text{ kg} \]

### Step 2: Use the mass of an electron
The mass of an electron is given as \(9.1 \times 10^{-31}\) kg.

### Step 3: Calculate the number of electrons
To find the number of electrons (N) in the total mass (M), we use the formula:
\[ N = \frac{M}{\text{mass of one electron}} \]
Substituting the values we have:
\[ N = \frac{1 \times 10^{-6} \text{ kg}}{9.1 \times 10^{-31} \text{ kg}} \]

### Step 4: Perform the division
Calculating the division:
\[ N = \frac{1}{9.1} \times 10^{(-6) - (-31)} = \frac{1}{9.1} \times 10^{25} \]
Calculating \( \frac{1}{9.1} \approx 0.109\):
\[ N \approx 0.109 \times 10^{25} \]

### Step 5: Express the final answer in scientific notation
To express \(0.109\) in scientific notation:
\[ 0.109 = 1.09 \times 10^{-1} \]
Thus,
\[ N \approx 1.09 \times 10^{-1} \times 10^{25} = 1.09 \times 10^{24} \]

### Final Answer
The number of electrons in 1 mg is approximately \(1.09 \times 10^{24}\).

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