Import Question JSON

Current Question (ID: 20895)

Question:

$\text{The radius of the second orbit of the } \text{Li}^{2+} \text{ ion is } x. \text{ What will be the radius of the third orbit of the } \text{Be}^{3+} \text{ ion?}$

Options:

1. $\frac{27x}{16}$
2. $\frac{16x}{27}$
3. $\frac{4x}{3}$
4. $\frac{3x}{4}$

Solution:

$r = a_0 \cdot \frac{n^2}{Z}$ $r_{\text{Li}^{2+}} = r_0 \times \frac{2^2}{3} = \frac{4r_0}{3} = x \Rightarrow r_0 = \frac{3x}{4}$ $r_{\text{Be}^{3+}} = r_0 \times \frac{3^2}{4} = \frac{9r_0}{4} = \frac{9 \times 3 \times x}{4 \times 4} = \frac{27x}{16}$

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
}