Import Question JSON

Current Question (ID: 20889)

Question:

$\text{Uncertainty in the position of a moving particle is } 10^{-7} \text{ m and uncertainty velocity is } 2.4 \times 10^{-24} \text{ m/sec, then the mass of a particle is } [X] \times 10^{-5} \text{ kg. The value of } X \text{ is:}$ $\text{[Report your answer to the nearest integer]}$

Options:

1. 26
2. 19
3. 28
4. 22

Solution:

$\text{According to Heisenberg uncertainty Principle}$ $\Delta X \times \Delta P \geq \frac{h}{4\pi}$ $\Rightarrow 10^{-7} \times m \times \Delta V = \frac{6.62 \times 10^{-34}}{4 \times 3.14}$ $\Rightarrow 10^{-7} \times m \times 2.4 \times 10^{-24} = \frac{6.62 \times 10^{-34}}{4 \times 3.14}$ $M = 0.2196 \times 10^{-3} \text{ kg}$ $= 21.96 \times 10^{-5} \text{ kg}$ $= 22$

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
}