Import Question JSON

Current Question (ID: 7480)

Question:

$\text{If the photon detector receives a total of } 3.15 \times 10^{-18} \text{ J from the radiation of 600 nm, the number of photons received by the detector would be:}$

Options:

1. $10^2$
2. $10$
3. $50$
4. $20$

Solution:

$\text{Hint: } E = \frac{hc}{\lambda}$ $\text{Step 1:}$ $\text{From the expression of the energy of one photon (E),}$ $E = \frac{hc}{\lambda}$ $\text{Where, } \lambda = \text{wavelength of radiation; } h = \text{Planck's constant; } c = \text{velocity of radiation}$ $\text{Substituting the values in the given expression of E:}$ $E = \frac{(6.626 \times 10^{-34} \text{ Js})(3 \times 10^8 \text{ ms}^{-1})}{(600 \times 10^{-9} \text{ m})} = 3.313 \times 10^{-19} \text{ J}$ $\text{The energy of one photon} = 3.313 \times 10^{-19} \text{ J}$ $\text{Number of photons received with } 3.15 \times 10^{-18} \text{ J} = \frac{3.15 \times 10^{-18} \text{ J}}{3.313 \times 10^{-19} \text{ J}} = 10$ $\text{Hence, option second is the correct answer.}$

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
}