Import Question JSON

Current Question (ID: 7508)

Question:

$\text{The wavelength of the spectral line obtained in the spectrum of Li}^{+2} \text{ when the transition takes place between levels whose sum is 4 and the difference is 2, will be:}$

Options:

1. $11.4 \times 10^{-6} \text{ cm}$
2. $1.14 \times 10^{-6} \text{ cm}$
3. $0.114 \times 10^{-6} \text{ cm}$
4. $1.14 \times 10^{-8} \text{ cm}$

Solution:

$\text{Hint: Calculation of wavelength in the Hydrogen spectrum using Rydberg's constant formula}$\n\n$\text{Explanation:}$\n\n$Z = 3$\n\n$n_1 + n_2 = 4$\n\n$n_1 - n_2 = 2$\n\n$n_1 = 1, n_2 = 3$\n\n$\frac{1}{\lambda} = R(Z) \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} \right]$\n\n$\frac{1}{\lambda} = 10967 \times (3)^2 \left[ \frac{1}{(1)^2} - \frac{1}{(3)^2} \right]$\n\n$\frac{1}{\lambda} = 10967 \times 9 \times \frac{8}{9}$\n\n$\lambda = \frac{1}{10967 \times 8} = 1.14 \times 10^{-8} \text{ m}$\n\n$= 1.14 \times 10^{-6} \text{ cm}$

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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
}