Import Question JSON

Current Question (ID: 20882)

Question:

$\text{A gas absorbs a photon of } 355 \text{ nm and emits at two wavelengths. If one of the emissions is at } 680 \text{ nm, the other is at:}$

Options:

1. $1035 \text{ nm}$
2. $325 \text{ nm}$
3. $743 \text{ nm}$
4. $518 \text{ nm}$

Solution:

$\text{Hint: The total energy of the photon remains conserved.}$ $\text{When energy of a photon is conserved, total energy is equal to the sum of energy of two photons.}$ $E(\text{total energy}) = E_1 + E_2$ $\frac{hc}{\lambda} = \frac{hc}{\lambda_1} + \frac{hc}{\lambda_2}$ $\frac{1}{\lambda} = \frac{1}{\lambda_1} + \frac{1}{\lambda_2}$ $\frac{1}{355} = \frac{1}{680} + \frac{1}{\lambda_2}$ $\lambda_2 = 743 \text{ nm}$

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
}