Import Question JSON

Current Question (ID: 7479)

Question:

$\text{A nitrogen laser produces radiation at a wavelength of 337.1 nm. If the number of photons emitted is } 5.6 \times 10^{24}\text{, the power of the laser is:}$

Options:

1. $4.56 \times 10^7 \text{ J}$
2. $3.33 \times 10^6 \text{ J}$
3. $1.29 \times 10^6 \text{ J}$
4. $9.17 \times 10^5 \text{ J}$

Solution:

$\text{Hint: Power} = \frac{Nhc}{\lambda}$ $\text{Step 1:}$ $\text{Power of laser = Energy with which it emits photons}$ $\text{Power} = \frac{Nhc}{\lambda}$ $\text{where N = number of photons emitted}$ $\text{h = Planck's constant}$ $\text{c = velocity of radiation}$ $\lambda = \text{wavelength of radiation}$ $\text{Step 2:}$ $\text{Substituting the values in the given expression of Energy (E):}$ $E = \frac{(5.6 \times 10^{24})(6.626 \times 10^{-34} \text{ Js})(3 \times 10^8 \text{ ms}^{-1})}{(337.1 \times 10^{-9} \text{ m})}$ $\text{Hence, the power of the laser is } 3.33 \times 10^6 \text{ J}$

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
}