Import Question JSON

Current Question (ID: 16395)

Question:

$\text{The acceleration of an electron due to the mutual attraction between the electron and a proton when they are } 1.6 \, \text{\AA} \text{ apart is:}$ $\left( \frac{1}{4\pi\varepsilon_0} \right) = 9 \times 10^9 \, \text{Nm}^2\text{C}^{-2}$

Options:

1. $10^{24} \, \text{m/s}^2$
2. $10^{23} \, \text{m/s}^2$
3. $10^{22} \, \text{m/s}^2$
4. $10^{25} \, \text{m/s}^2$

Solution:

$\text{Hint: } F = \frac{kq_1q_2}{r^2}$ $\text{Step: Find the acceleration of the electron.}$ $F = \frac{ke^2}{r^2}$ $ma = \frac{ke^2}{r^2}$ $\Rightarrow a = \frac{ke^2}{mr^2}$ $a = 9 \times 10^9 \times \frac{(1.6 \times 10^{-19})^2}{(1.6 \times 10^{-10})^2 \times (9 \times 10^{-31})}$ $\Rightarrow a = 10^{-29} \times 10^{51} = 10^{22} \, \text{m/s}^2$ $\text{Hence, option (3) is the correct answer.}$

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
}