Import Question JSON

Current Question (ID: 17928)

Question:

$\text{An element has a body-centered cubic (BCC) structure with a cell edge of } 288 \text{ pm. The atomic radius is:}$

Options:

1. $\frac{\sqrt{2}}{4} \times 288 \text{ pm}$
2. $\frac{4}{\sqrt{3}} \times 288 \text{ pm}$
3. $\frac{4}{\sqrt{2}} \times 288 \text{ pm}$
4. $\frac{\sqrt{3}}{4} \times 288 \text{ pm}$

Solution:

$\text{HINT: For BCC lattice, } 4r = a\sqrt{3}$ $\text{Explanation: We know that, for BCC lattice:}$ $4r = a\sqrt{3}, \text{ where 'a' is the edge length and 'r' is the atomic radius.}$ $\text{Given, } a = 288 \text{ pm}$ $r = \frac{a\sqrt{3}}{4} = \frac{\sqrt{3}}{4} \times 288$

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
}