Import Question JSON

Current Question (ID: 10773)

Question:

$\text{A piece of iron is heated in a flame. If it becomes dull red first, then becomes reddish yellow, and finally turns to white hot, the correct explanation for the above observation is possible by using:}$

Options:

1. $\text{Stefan's law}$
2. $\text{Wien's displacement law}$ (Correct)
3. $\text{Kirchhoff's law}$
4. $\text{Newton's law of cooling}$

Solution:

\text{According to Wien's displacement law, } \lambda_m T = \text{constant. So, as temperature T increases, the dominant wavelength } \lambda_m \text{ decreases.} \text{When iron is heated:} \text{1. At lower temperature: Peak emission is at longer wavelengths (red region) - appears dull red} \text{2. At medium temperature: Peak shifts to shorter wavelengths (yellow-orange region) - appears reddish yellow} \text{3. At high temperature: Peak shifts to even shorter wavelengths (blue-white region) - appears white hot} \text{This color progression from red → yellow → white as temperature increases is perfectly explained by Wien's displacement law, which relates the peak wavelength of blackbody radiation to temperature.} \text{Hence, the correct answer is option 2.}

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
}