Question
At equilibrium spacing in a crystalline solid, which of the following is true for net inter-atomic force (F) and potential energy (U)
The correct answer is
F is zero and U is minimum
To understand the equilibrium spacing in a crystalline solid, we need to consider the concepts of net inter-atomic force and potential energy:
- Net Inter-atomic Force (F): At equilibrium, the attractive and repulsive forces between atoms balance out, resulting in a net force of zero (\(F = 0\)).
- Potential Energy (U): When atoms are at equilibrium spacing, the potential energy between them is minimized. This is because any deviation from the equilibrium would require an increase in energy to overcome the forces keeping the atoms at this distance.
Now, let's evaluate the given options:
- Option 1: F is zero and U is zero - This is incorrect because while the net force is zero, the potential energy is not zero.
- Option 2: F is zero and U is minimum - This is correct because, at equilibrium, the net force is zero, and the potential energy is at its minimum.
- Option 3: F is minimum and U is zero - This is incorrect because the net force is zero, not minimum, and the potential energy is not zero.
- Option 4: F is minimum and U is minimum - This is incorrect because the net force is zero, not minimum.
Therefore, the correct answer is that at equilibrium spacing in a crystalline solid, the net inter-atomic force is zero, and the potential energy is at its minimum.
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Important Questions from Crystal Structure Density Atomic Packing Factor
- Match the crystal systems in Column I with the corresponding axial lengths (a, b, c) and interaxial angles ($\alpha$, $\beta$, $\gamma$) provided in Column II
Column I Column II (P) Tetragonal (1) $a \neq b \neq c$, $\alpha = \beta = \gamma = 90^\circ$ (Q) Rhombohedral (2) $a = b \neq c$, $\alpha = \beta = \gamma = 90^\circ$ (R) Orthorhombic (3) $a \neq b \neq c$, $\alpha = \gamma = 90^\circ \neq \beta$ (S) Monoclinic (4) $a = b = c$, $\alpha = \beta = \gamma \neq 90^\circ$ - The coordination number for an octahedral site in pure copper is __________.
The lattice parameter of face-centered cubic iron ($\gamma$-Fe) is 0.3571 nm. The radius (in nm) of the octahedral void in $\gamma$-Fe is _______________
- For a bcc metal the ratio of the surface energy per unit area of the (100) plane to that of the (110) plane is ________
- Pure iron transforms from body centered cubic (BCC) to face centered cubic (FCC) crystal structure at $912 \text{ °C}$. If the lattice parameter of the BCC phase is $0.293 \text{ nm}$ and that of the FCC phase is $0.363 \text{ nm}$, the associated volume change is ________ (in % to one decimal place)
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