Question 35 of 62beginner🔧 ApplyNumerical2 marks

If the diameter of a carbon atom is 0.15 nm, calculate the number of carbon atoms which can be placed side by side in a straight line across length of length 20 cm long.

Correct Answer

1.33×1091.33 \times 10^9 atoms

Exercise: EXERCISES | Q: 2.35 | (Page 41)
For More Understanding

Explanation

To find the number of carbon atoms that can be placed side by side, we divide the total length of the line by the diameter of a single carbon atom. It is crucial to ensure both measurements are in the same units before dividing.

Solution Steps

  1. Given: Diameter of carbon atom = 0.15 nm0.15 \text{ nm} and Total length = 20 cm20 \text{ cm}

  2. Step 1: Convert the diameter of the carbon atom into cm. We know that 1 nm=10−9 m=10−7 cm1 \text{ nm} = 10^{-9} \text{ m} = 10^{-7} \text{ cm}. Therefore, Diameter = 0.15×10−7 cm=1.5×10−8 cm0.15 \times 10^{-7} \text{ cm} = 1.5 \times 10^{-8} \text{ cm}

  3. Step 2: Calculate the number of carbon atoms. Number of atoms = Total lengthDiameter of one atom\frac{\text{Total length}}{\text{Diameter of one atom}} Number of atoms = 20 cm1.5×10−8 cm\frac{20 \text{ cm}}{1.5 \times 10^{-8} \text{ cm}}

  4. Step 3: Simplify the expression. Number of atoms = 201.5×108=13.33×108=1.33×109\frac{20}{1.5} \times 10^8 = 13.33 \times 10^8 = 1.33 \times 10^9 atoms

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