Import Question JSON

Current Question (ID: 19641)

Question:

$\text{For an object radiating heat at } 300 \text{ K, the wavelength corresponding to maximum intensity is } \lambda. \text{ When the temperature of the body increases by } 300 \text{ K, the new wavelength corresponding to maximum intensity becomes:}$

Options:

1. $\frac{\lambda}{2}$
2. $2\lambda$
3. $\lambda$
4. $\frac{5\lambda}{2}$

Solution:

$\text{Hint: } \lambda_m T = \text{constant.}$ $\text{Step: Find the new wavelength corresponding to maximum intensity.}$ $\text{According to Wien's Displacement Law: } \lambda_m T = \text{constant}$ $\text{Given:}$ $\text{The initial temperature } T_1 = 300 \text{ K, and corresponding wavelength is } \lambda_1 = \lambda.$ $\text{The new temperature of the object is}$ $T_2 = 300 \text{ K} + 300 \text{ K} = 600 \text{ K.}$ $\text{Since } \lambda_m T = \text{constant, we can write: } \lambda_1 T_1 = \lambda_2 T_2$ $\Rightarrow \frac{\lambda_1}{\lambda_2} = \frac{T_2}{T_1}$ $\Rightarrow \lambda_2 = \lambda \left( \frac{300}{600} \right) = \frac{\lambda}{2}$ $\text{Hence, option (1) is the correct answer.}$

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
}