Import Question JSON

Current Question (ID: 20897)

Question:

$\text{A hydrogen atom in its ground state absorbs 12.75 eV of energy. The orbital angular momentum of the electron becomes } \frac{nh}{2\pi}. \text{ What is the value of } n?$

Options:

1. $3$
2. $4$
3. $5$
4. $2$

Solution:

$\text{Given, } \Delta E = 12.75 \text{ eV and } n_1 = 1$ $\text{We know that, } \Delta E = 13.6 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$ $\text{So, } \Delta E = 13.6 \left( 1 - \frac{1}{n^2} \right) = 12.75$ $\Rightarrow -\frac{1}{n^2} = \frac{12.75}{13.6} - 1$ $n^2 = 16 \Rightarrow n = 4$ $\text{Thus, the correct answer is option 2.}$

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
}