Import Question JSON

Current Question (ID: 7452)

Question:

$\text{The wave number of a light whose time period is } 2.0 \times 10^{-10} \text{ s would be:}$

Options:

1. $16.66 \text{ m}^{-1}$
2. $1.66 \text{ m}^{-1}$
3. $32.34 \text{ m}^{-1}$
4. $12.34 \text{ m}^{-1}$

Solution:

$\text{Hint: Wavelength of light } (\lambda) = \frac{c}{\nu}$ $\text{STEP 1: Find out the frequency from given data}$ $\text{Frequency } (\nu) \text{ of light} = \frac{1}{\text{Period}} = \frac{1}{2.0} \times 10^{10} = 5.0 \times 10^9 \text{ s}^{-1}$ $\text{STEP 2: Calculate wavelength of light using frequency and velocity of light.}$ $\text{Wavelength of light } (\lambda) = \frac{c}{\nu}$ $\text{where, } c \text{ is velocity of light in vacuum} = 3.0 \times 10^8 \text{ ms}^{-1}$ $\text{Wave length of light, } (\lambda) = \frac{3.0 \times 10^8 \text{ ms}^{-1}}{5.0 \times 10^9 \text{ s}^{-1}} = 6.0 \times 10^{-2} \text{ m}$ $\text{STEP 3: Calculate wave number from wavelength}$ $\text{Wave number of light } (\overline{\nu}) = \frac{1}{\lambda} = \frac{1}{6.0 \times 10^{-2}} = 16.66 \text{ m}^{-1}$

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
}