Question 36 of 62beginner🔧 ApplyNumerical2 marks

2×102 \times 10⁸ atoms of carbon are arranged side by side. Calculate the radius of carbon atom if the length of this arrangement is 2.4 cm.

Correct Answer

The radius of the carbon atom is 6×10−96 \times 10^{-9} cm or 60 pm.

Exercise: EXERCISES | Q: 2.36 | (Page 41)
For More Understanding

Explanation

To find the radius of a single carbon atom, we first determine its diameter by dividing the total length of the arrangement by the total number of atoms placed side by side. Since radius is half of the diameter, we then divide the obtained diameter by 2. Finally, the value is converted to picometers (pm) for a standard atomic scale representation.

Solution Steps

  1. Step 1: Calculate the diameter of a single carbon atom by dividing the total length by the number of atoms. Diameter = 2.4 cm2×108=1.2×10−8\frac{2.4 \text{ cm}}{2 \times 10^8} = 1.2 \times 10^{-8} cm

  2. Step 2: Calculate the radius of the carbon atom, which is half of its diameter. Radius = 1.2×10−8 cm2=0.6×10−8\frac{1.2 \times 10^{-8} \text{ cm}}{2} = 0.6 \times 10^{-8} cm = 6×10−96 \times 10^{-9} cm

  3. Step 3: Convert the radius into picometers (pm) for standard representation. Since 1 cm=10101 \text{ cm} = 10^{10} pm, Radius = 6×10−9 cm×1010 pm/cm=606 \times 10^{-9} \text{ cm} \times 10^{10} \text{ pm/cm} = 60 pm

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