Import Question JSON

Current Question (ID: 10811)

Question:

$\text{A black body at 200 K is found to emit maximum energy at a wavelength of 14 } \mu\text{m. When its temperature is raised to 1000 K, the wavelength at which maximum energy is emitted will be:}$

Options:

1. $14 \mu\text{m}$
2. $70 \mu\text{m}$
3. $2.8 \mu\text{m}$ (Correct)
4. $2.8 \text{ nm}$

Solution:

\text{According to Wien's displacement law: } \lambda_{m1} T_1 = \lambda_{m2} T_2. \text{ Therefore: } \lambda_{m2} = \frac{\lambda_{m1} T_1}{T_2} = \frac{14 \times 200}{1000} = 2.8 \mu\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
}