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Current Question (ID: 17958)

Question:

$\text{The edge lengths of the unit cells in terms of the radius of spheres constituting}$ $\text{fcc, bcc, and simple cubic unit cells are respectively -}$

Options:

1. $2\sqrt{2}r, \frac{4r}{\sqrt{3}}, 2r$
2. $\frac{4r}{\sqrt{3}}, 2\sqrt{2}r, 2r$
3. $2r, 2\sqrt{2}r, \frac{4r}{\sqrt{3}}$
4. $2r, \frac{4r}{\sqrt{3}}, 2\sqrt{2}r$

Solution:

$\text{HINT: Check the relation between edge length and radius of an atom.}$ $\text{Explanation:}$ $\text{Edge length for different types of unit cells can be tabulated as}$ $\text{Types of the unit cell} \quad \text{Edge length}$ $\text{Fcc} \quad 2\sqrt{2}r$ $\text{Bcc} \quad \frac{4}{\sqrt{3}}r$ $\text{Simple cubic unit} \quad 2r$

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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
}