A sample of toothpaste weighing 500g. On analysis was found to certain 0.2 g of fluorine. The concentration of fluorine in ppm is

Options

A. `4 times 10^3`
B. `4 times 10^2`
C. `4 times 10`
D. `2 times 10^2`

Answer

To find the concentration of fluorine in parts per million (ppm) in the given sample of toothpaste, we can follow these steps:

### Step 1: Understand the formula for ppm
The formula to calculate concentration in ppm is given by:

\[ \text{ppm} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 10^6 \]

### Step 2: Identify the values from the question
From the question, we have:
- Mass of solute (fluorine) = 0.2 g
- Mass of solution (toothpaste) = 500 g

### Step 3: Substitute the values into the ppm formula
Now, we can substitute the values into the ppm formula:

\[ \text{ppm} = \left( \frac{0.2 \, \text{g}}{500 \, \text{g}} \right) \times 10^6 \]

### Step 4: Calculate the fraction
Calculating the fraction:

\[ \frac{0.2}{500} = 0.0004 \]

### Step 5: Multiply by \(10^6\)
Now, we multiply by \(10^6\):

\[ \text{ppm} = 0.0004 \times 10^6 = 400 \]

### Step 6: Express in scientific notation
Expressing 400 in scientific notation:

\[ 400 = 4 \times 10^2 \]

### Conclusion
Thus, the concentration of fluorine in ppm is \(4 \times 10^2\).

### Final Answer
The correct option is **B: \(4 \times 10^2\)**.

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