Import Question JSON

Current Question (ID: 20901)

Question:

$\text{The ionization energy of a hydrogen atom is } 13.6 \text{ eV. What is the ionization energy of a } \text{Li}^{2+} \text{ ion?}$

Options:

1. $54.4 \text{ eV}$
2. $122.4 \text{ eV}$
3. $13.6 \text{ eV}$
4. $3.4 \text{ eV}$

Solution:

$\text{Ionisation energy } = 13.6 \frac{z^2}{n^2} \text{ eV}$ $\text{[Since ionisation energy is defined for ground state only, thus } n=1]$ $\text{Thus,}$ $\text{Ionisation energy (I. E)} \propto Z^2$ $\therefore \frac{I \cdot E_H}{I \cdot E_{\text{Li}^{2+}}} = \frac{z_H^2}{z_{\text{Li}^{2+}}^2}$ $\Rightarrow I \cdot E_{\text{Li}^{2+}} = (I \cdot E)_H \frac{z_{\text{Li}^{2+}}^2}{z_H^2}$ $\text{Therefore, the ionisation energy of } \text{Li}^{2+} \text{ ion}$ $= 13.6 \times \frac{3^2}{1^2} \text{ eV} = 122.4 \text{ eV}$

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
}