Question:
A binary solid has a primitive cubical structure with B$^-$ ions constituting the lattice points and A$^+$ ions occupying 25% of its tetrahedral holes. The molecular formula of the crystal is
A binary solid has a primitive cubical structure with B$^-$ ions constituting the lattice points and A$^+$ ions occupying 25% of its tetrahedral holes. The molecular formula of the crystal is
Show Hint
Tetrahedral voids = 2 × number of atoms in unit cell.
Updated On: May 8, 2026
- A$_2$B
- AB$_3$
- AB$_2$
- A$_2$B$_3$
- A$_2$B$_5$
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
• Primitive cubic lattice has 1 atom per unit cell.
• Number of tetrahedral voids = 2 × number of lattice points.
Step 1: Count B$^-$ ions.
Primitive cubic → 1 lattice point → 1 B$^-$ ion.
Step 2: Count tetrahedral voids. \[ \text{Void} = 2 \times 1 = 2 \]
Step 3: A$^+$ ions occupying 25%. \[ 25% \text{ of 2} = \frac{1}{2} \]
Step 4: Ratio of A to B. \[ A : B = \frac{1}{2} : 1 = 1 : 2 \]
Step 5: Final formula. \[ \boxed{AB_2} \]
• Primitive cubic lattice has 1 atom per unit cell.
• Number of tetrahedral voids = 2 × number of lattice points.
Step 1: Count B$^-$ ions.
Primitive cubic → 1 lattice point → 1 B$^-$ ion.
Step 2: Count tetrahedral voids. \[ \text{Void} = 2 \times 1 = 2 \]
Step 3: A$^+$ ions occupying 25%. \[ 25% \text{ of 2} = \frac{1}{2} \]
Step 4: Ratio of A to B. \[ A : B = \frac{1}{2} : 1 = 1 : 2 \]
Step 5: Final formula. \[ \boxed{AB_2} \]
Was this answer helpful?
0
0
Top KEAM Chemistry Questions
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
- $4\, g$ of copper was dissolved in concentrated nitric acid. The copper nitrate solution on strong heating gave $5\, g$ of its oxide. The equivalent weight of copper is :
- Green chemistry deals with
- Neopentyl bromide undergoes dehydrohalogenation to give alkenes even though it has no $\beta$- hydrogen. This is due to
- Plot of $ log\text{ }x/m $ against log $p$ is a straight line inclined at an angle of $ 45{}^\circ $ . When the pressure is $ 0.5 \,arm $ and Freundlich parameter. $ k $ is $ 10 $ , the amount of solute adsorbed per gram of adsorbent will be $ (log\text{ }5=0.6990) $
View More Questions
Top KEAM The solid state Questions
- Substance which is weakly repelled by a magnetic field is
- A binary solid has a primitive cubical structure with $B^-$ ions constituting the lattice points and $A^+$ ions occupying $25\%$ of its tetrahedral holes. The molecular formula of the crystal is
- For two isomorphous crystals $A$ and $B$, the ratio of density of $A$ to that of $B$ is $1.6$ while the ratio of the edge length of $B$ to that of $A$ is $2$. If the molar mass of crystal $B$ is $200\,g\,mol^{-1}$, then that of crystal $A$ is
- Which one of the following has a different crystal lattice from those of the rest?
- Aluminium (atomic mass = $27$) crystallizes in a cubic system with edge length of $4 \, ?$. Its density is $2.7 \,g \,cm^{-3}$. The number of aluminium atoms present per unit cell is
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions