Import Question JSON

Current Question (ID: 11178)

Question:

$\text{The mean free path } l \text{ for a gas molecule depends upon the diameter, } d \text{ of the molecule as:}$

Options:

1. $l \propto \frac{1}{d^2}$ (Correct)
2. $l \propto d$
3. $l \propto d^2$
4. $l \propto \frac{1}{d}$

Solution:

$\text{Hint: Use the formula of the mean free path.}$ $\text{Step 1: Find the mean free path.}$ $l = \frac{1}{\sqrt{2\pi d^2 n}} \propto \frac{1}{d^2}$ $\lambda = \text{mean free path}$ $d = \text{effective diameter of the molecule}$ $n = \text{number density of molecules}$

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
}