Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: When a material is reduced to nanoscale, its surface area to volume ratio increases significantly. Reason R: At the nanoscale, the size of the nanoparticles decrease, causing a larger fraction of atoms or molecules to be present on the surface compared to bulk. In the light of the above statements, choose the most appropriate answer from the options given below
• Both A and R are correct and R is the correct explanation of A
• Both A and R are correct but R is NOT the correct explanation of A
• A is correct but R is not correct
• A is not correct but R is correct

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

At nanoscale:
• Particle size decreases drastically.
• Surface atoms become dominant.
• Surface area to volume ratio increases enormously. This is why nanoparticles are highly reactive and efficient catalysts.

Answer 1

The Correct Option is A

Concept: Nanoscience deals with materials whose dimensions lie approximately in the range: \[ 1\,\text{nm} \text{ to } 100\,\text{nm} \] At nanoscale dimensions, materials begin to show properties very different from their bulk counterparts. One of the most important reasons behind these unusual properties is the very large: \[ \boxed{\text{Surface Area to Volume Ratio}} \] As the size of a particle decreases:
• Volume decreases rapidly.
• Surface atoms become comparatively more significant.
• A large fraction of atoms remain exposed on the surface. This is responsible for many nanoscale properties such as:
• High reactivity
• Increased catalytic activity
• Greater adsorption
• Altered melting point

Step 1: Examine Assertion A carefully. Assertion A states: “When a material is reduced to nanoscale, its surface area to volume ratio increases significantly.” This statement is absolutely correct. To understand this mathematically, consider a cube of side \(a\). Surface area: \[ 6a^2 \] Volume: \[ a^3 \] Thus: :contentReference[oaicite:0]{index=0} From this relation:
• As \(a\) decreases, \(\frac{6}{a}\) increases.
• Therefore, smaller particles possess larger surface area relative to their volume. At nanoscale dimensions, this increase becomes extremely large. Hence, Assertion A is correct.

Step 2: Examine Reason R carefully. Reason R states: “At the nanoscale, the size of nanoparticles decreases, causing a larger fraction of atoms or molecules to be present on the surface compared to bulk.” This statement is also correct. In bulk materials:
• Most atoms remain inside the material.
• Only a small fraction lies on the surface. But when particle size decreases drastically:
• Interior atoms decrease in proportion.
• Surface atoms become dominant. Thus, nanoparticles contain a much greater proportion of surface atoms. Hence, Reason R is correct.

Step 3: Check whether R correctly explains A. Now we determine whether the reason properly explains the assertion. Assertion says: \[ \text{Surface area to volume ratio increases} \] Reason explains: \[ \text{Smaller particles have more atoms on the surface} \] This is exactly the physical explanation behind the increase in surface area to volume ratio. Therefore:
• Assertion is true.
• Reason is true.
• Reason correctly explains Assertion. Final Conclusion: Both Assertion A and Reason R are correct, and Reason R correctly explains Assertion A. Hence, the correct answer is: \[ \boxed{(1)} \]