QQuestionChemistry
QuestionChemistry
The atomic radius of iron is 0.125 nm, while that of a carbon atom is 0.070 nm. Can a carbon atom fit inside a steel BCC structure without distorting the neighboring atoms?
True or False
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the Body-Centered Cubic (BCC) Structure
- In a BCC structure, atoms are located at each corner of the cubic unit cell and one atom at the center - The size of the interstitial space depends on the atomic radii of the atoms in the structure
Step 3:: Calculate the Size of the Interstitial Space
- In a BCC structure, the interstitial site is located at the center of the unit cell - The size of this space depends on the atomic radius of the host atoms (iron in this case)
Step 4:: Determine the Interstitial Space Radius
- Atomic radius of iron = $$0.125 \times 10^{-9} \mathrm{m}
- The interstitial space radius can be calculated using geometric considerations - Typically, the interstitial space radius is approximately 0.414 times the host atom's radius
Step 5:: Calculate the Interstitial Space Radius
r_{\mathrm{interstitial}} = 0.414 \times r_{\mathrm{Fe}} = 0.414 \times (0.125 \times 10^{-9}) = 0.0518 \times 10^{-9} \mathrm{m}
Step 6:: Compare with Carbon Atom Radius
- Carbon atom radius = $$0.070 \times 10^{-9} \mathrm{m}
- Interstitial space radius = 0.0518 \times 10^{- 9} \mathrm{m}
Step 7:: Determine if Carbon Can Fit
- Carbon atom radius ($$0.070 \times 10^{-9} \mathrm{m}$$) is larger than the interstitial space radius ($$0.0518 \times 10^{-9} \mathrm{m}$$)
- This means the carbon atom would distort the neighboring iron atoms
Final Answer
A carbon atom cannot fit inside a steel BCC structure without distorting the neighboring atoms.
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