Import Question JSON

Current Question (ID: 20910)

Question:

$\text{The de Broglie wavelength of an electron in the 4}^{\text{th}} \text{ orbit is:}$ $\text{(where, } a_0 = \text{radius of 1}^{\text{st}} \text{ orbit)}$

Options:

1. $2\pi a_0$
2. $8\pi a_0$
3. $6\pi a_0$
4. $4\pi a_0$

Solution:

$\text{Hint: } \lambda = \frac{h}{P}$ $\therefore \lambda_{\text{de-Broglie}} = \frac{2\pi r}{n} = \frac{2\pi}{n} \times 0.529 \frac{n^2}{z} A$ $\lambda_{\text{de-Broglie}} = 2\pi \times n \times a_0$ $\text{or, } = 2\pi \times 4 \times a_0$ $= 8\pi a_0 A$

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
}