Import Question JSON

Current Question (ID: 7450)

Question:

$2 \times 10^8 \text{ atoms of carbon are arranged side by side. The radius of a carbon atom if the length of this arrangement is 2.4 cm would be:}$

Options:

1. $7.0 \times 10^{-11} \text{ m}$
2. $5.0 \times 10^{-11} \text{ m}$
3. $8.0 \times 10^{-11} \text{ m}$
4. $6.0 \times 10^{-11} \text{ m}$

Solution:

$\text{HINT: Diameter of carbon atom can be calculated by using length and number of carbon atoms from which radius of carbon atoms can be calculated.}$ $\text{Step 1:}$ $\text{Length of the given arrangement} = 2.4 \text{ cm}$ $\text{Number of carbon atoms present} = 2 \times 10^8$ $\therefore \text{Diameter of carbon atom} = \frac{2.4}{2 \times 10^8} \text{ cm} = 1.2 \times 10^{-8} \text{ cm} = 1.2 \times 10^{-10} \text{ m}$ $\text{Step 2:}$ $\text{Radius of carbon atom} = \frac{\text{Diameter}}{2} = \frac{1.2 \times 10^{-10}}{2} \text{ m} = 6.0 \times 10^{-11} \text{ m}$

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
}