Import Question JSON

Current Question (ID: 19876)

Question:

$\text{The root mean square speed of smoke particles of mass } 5 \times 10^{-17} \text{ kg}$ $\text{in their Brownian motion in air at NTP is, approximately:}$ $\left[ \text{Given } k = 1.38 \times 10^{-23} \text{ JK}^{-1} \right]$

Options:

1. $60 \text{ mm s}^{-1}$
2. $12 \text{ mm s}^{-1}$
3. $15 \text{ mm s}^{-1}$
4. $36 \text{ mm s}^{-1}$

Solution:

$\text{The root mean square speed is given by } v_{rms} = \sqrt{\frac{3kT}{m}}$ $\text{At NTP, } T = 273 \text{ K}$ $v_{rms} = \sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 273}{5 \times 10^{-17}}}$ $= 15 \text{ mm s}^{-1}$

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
}