Import Question JSON

Current Question (ID: 17918)

Question:

$\text{Aluminum crystallizes in a cubic close-packed structure. It's metallic radius is } 125 \text{ pm. The number of unit cells in } 1.00 \text{ cm}^3 \text{ of aluminum are:}$

Options:

1. $2.27 \times 10^{22}$
2. $3.54 \times 10^{22}$
3. $4.54 \times 10^{22}$
4. $1.27 \times 10^{20}$

Solution:

$\text{HINT: For cubic closed-packed structure, } a = 2\sqrt{2}r$ $\text{STEP 1: Calculate the length of the side}$ $a = 2\sqrt{2}r = 2\sqrt{2} \times 125 \text{ pm} = 353.55 \text{ pm} \approx 354 \text{ pm}$ $\text{STEP 2: Calculate the number of unit cells}$ $\text{The volume of the unit cell is } a^3$ $\text{The volume of one unit cell} = 354 \text{ pm} = 354 \times 10^{-10} \text{ cm}$ $= (354 \times 10^{-10})^3 \text{ cm}^3 = 4.43 \times 10^{-23} \text{ cm}^3$ $\text{Therefore, the number of unit cells in } 1.00 \text{ cm}^3 = \frac{1.00 \text{ cm}^3}{4.43 \times 10^{-23} \text{ cm}^3} = 2.27 \times 10^{22}$

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
}