Import Question JSON

Current Question (ID: 10777)

Question:

$\text{The energy distribution E with the wavelength } (\lambda) \text{ for the black body radiation at temperature T Kelvin is shown in the figure. As the temperature is increased the maxima will:}$

Options:

1. $\text{Shift towards left and become higher}$ (Correct)
2. $\text{Rise high but will not shift}$
3. $\text{Shift towards right and become higher}$
4. $\text{Shift towards left and the curve will become broader}$

Solution:

\text{According to Wien's displacement law } \lambda_m \propto \frac{1}{T}\text{.} \text{Hence, if temperature increases } \lambda_m \text{ decreases i.e., peak of the } E - \lambda \text{ curve shifts towards left.} \text{Additionally, according to Stefan-Boltzmann law, the total energy radiated is proportional to } T^4\text{, so when temperature increases, the peak also becomes higher.} \text{Therefore, when temperature is increased:} \text{1. The peak wavelength } \lambda_m \text{ decreases (shifts left)} \text{2. The peak intensity increases (becomes higher)} \text{This corresponds to option 1: Shift towards left and become higher.}

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
}