Import Question JSON

Current Question (ID: 16411)

Question:

$\text{An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius } r. \text{ The Coulomb force } \vec{F} \text{ on the electron is: (Where } K = \frac{1}{4\pi\varepsilon_0})$

Options:

1. $-K \frac{e^2}{r^3} \hat{r}$
2. $K \frac{e^2}{r^3} \vec{r}$
3. $-K \frac{e^2}{r^2} \vec{r}$
4. $K \frac{e^2}{r^2} \hat{r}$

Solution:

$\text{(3) } \vec{F} \rightarrow = -k \frac{e^2}{r^2} \hat{r} \quad (\text{Vector form})$ $= -k \frac{e^2}{r^3} r \rightarrow \quad (\because \hat{r} = \frac{r}{r}) \rightarrow r$

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
}