Import Question JSON

Current Question (ID: 17939)

Question:

$\text{An element occurring in the bcc structure has } 12.08 \times 10^{23} \text{ unit cells.}$ $\text{The total number of atoms of the element in these cells will be:}$

Options:

1. $24.16 \times 10^{23}$
2. $36.18 \times 10^{23}$
3. $6.04 \times 10^{23}$
4. $12.08 \times 10^{23}$

Solution:

$\text{In BCC structure, one unit cell has 2 atoms.}$ $\text{The unit cell is defined as the repeating unit of the crystal lattice.}$ $\text{These unit cells are identical in shape and form a sort of 3D arrangement of atoms,}$ $\text{molecules or the ions which are present in the crystal lattice.}$ $\text{So as we know that the bcc structure is made up of 2 atoms and we have to}$ $\text{find the number of atoms for } 12.08 \times 10^{23} \text{ unit cells.}$ $\text{So, 1 unit cell of bcc structure has = 2 atoms present in it.}$ $12.08 \times 10^{23} \text{ unit cells of bcc structure have } = 2 \times 12.08 \times 10^{23} = 24.16 \times 10^{23}$ $\text{Thus, the number of atoms present in } 12.08 \times 10^{23} \text{ unit cells}$ $\text{is } 24.16 \times 10^{23} \text{ atoms.}$

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
}