Import Question JSON

Current Question (ID: 18001)

Question:

$\text{If an element (at. Wt. = 50) crystallises in fcc lattice, with } a = 0.50 \text{ nm, then the density of unit cell if it contains } 0.25 \% \text{ Schottky defect is -}$ $\text{(Use } N_A = 6 \times 10^{23}\text{)}$

Options:

1. $2.0 \text{ g/cc}$
2. $2.66 \text{ g/cc}$
3. $3.06 \text{ g/cc}$
4. $\text{None of the above.}$

Solution:

$\text{In Schottky defect, density of of crystal decreases.}$ $\text{Density of crystal decreases due to Schottky defect.}$ $\text{Effective no. of atoms per unit cell in given lattice.}$ $= 4 \left(1 - \frac{0.25}{100}\right) = 3.99$ $p = \frac{50 \times 3.99}{6 \times 10^{23} \left(0.5 \times 10^{-7}\right)^3} = 2.66$

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
}