Import Question JSON

Current Question (ID: 17969)

Question:

$\text{Total volume of atoms present in a face centred cubic unit cell of a metal is -}$ $\text{(r is atomic radius)}$

Options:

1. $\frac{20}{3} \pi r^3$
2. $\frac{24}{3} \pi r^3$
3. $\frac{12}{3} \pi r^3$
4. $\frac{16}{3} \pi r^3$

Solution:

$\text{FCC contains 4 atoms per unit cell.}$ $\text{Volume of atoms in cell} = \frac{4}{3} \pi r^3 \times n \text{ (n = 4 for FCC)}$ $= \frac{4}{3} \times \pi r^3 \times 4 = \frac{16}{3} \times \pi r^3$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

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
}