Import Question JSON

Current Question (ID: 17972)

Question:

$\text{The incorrect statement among the following is:}$

Options:

1. $\text{The fraction of the total volume occupied by the atoms in a primitive cell is 0.48.}$
2. $\text{Molecular solids are generally volatile.}$
3. $\text{The number of carbon atoms in a unit cell of diamond is 8.}$
4. $\text{The number of Bravais lattices in which a crystal can be categorized is 14.}$

Solution:

$\text{HINT: Packing fraction of simple cube = 0.52}$ $\text{Explanation:}$ $\text{STEP 1:}$ $\text{Packing fraction of simple cube}$ $= \frac{z}{a^3} \times \frac{4}{3} \times \pi \times r^3 = \frac{1}{a^3} \times \frac{4}{3} \times \pi \times r^3 (2r)^3$ $= 0.52$ $\therefore \text{For primitive cell } a=2r$ $\text{Volume occupied = 52\%}$ $\text{STEP 2:}$ $\text{Diamond has FCC unit cell structure made up of C atoms.}$ $\text{This accounts for } 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \text{ C atoms}$ $\text{C atoms are also present in one half of the tetrahedral voids.}$ $\text{There are 8 tetrahedral voids in fcc structure.}$ $\text{This accounts for remaining } 8 \times \frac{1}{2} = 4 \text{ C atoms}$ $\text{Thus, total 4+4=8 C atoms are present per unit cell of diamond.}$

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Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}