Import Question JSON

Current Question (ID: 7481)

Question:

$\text{The neon gas emits radiation of 616 nm. The number of quanta that are present in 2 J of energy is:}$

Options:

1. $6.2 \times 10^{-18}$
2. $5.6 \times 10^{17}$
3. $6.2 \times 10^{18}$
4. $32.2 \times 10^{-20}$

Solution:

$\text{Hint: Number of quanta can be calculated using energy of one quantum.}$ $\text{Step 1: Find the frequency}$ $\nu = \frac{c}{\lambda}\text{; where } \nu \text{ is the frequency; } c = 3.0 \times 10^8 \text{ m/s and } \lambda = \text{wavelength}$ $\text{Thus, } \nu = \frac{3 \times 10^8 \text{ m/s}}{616 \times 10^{-9} \text{ m}} = 4.87 \times 10^{14} \text{ s}^{-1}$ $\text{Step 2: Calculate the energy of quanta}$ $\text{We know that; E = h}\nu$ $E = (6.63 \times 10^{-34} \text{ Js})(4.87 \times 10^{14} \text{ s}^{-1}) = 32.27 \times 10^{-20} \text{ J}$ $\text{This is the energy present in one quantum.}$ $\text{Step 3: Calculate the number of quanta}$ $\text{Number of quanta in 2J energy} = \frac{2}{32.27 \times 10^{-20}} \text{ J} = 6.2 \times 10^{18}$ $\text{Hence, option third is the correct answer.}$

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
}