Import Question JSON

Current Question (ID: 16389)

Question:

$10^9$ $\text{electrons move out of a body to another body every second, how much time approximately is required to get a total charge of } 1 \text{ C on the other body?}$

Options:

1. $200 \text{ years}$
2. $100 \text{ years}$
3. $150 \text{ years}$
4. $250 \text{ years}$

Solution:

$\text{Hint: Use the concept of charge quantization.}$ $\text{Step 1: Calculate the charge transferred per second.}$ $\text{In one second } 10^9 \text{ electrons move out of the body. Therefore the charge given out in one second is:}$ $1.6 \times 10^{-19} \times 10^9 \text{ C} = 1.6 \times 10^{-10} \text{ C.}$ $\text{Step 2: Find the time to transfer the charge.}$ $\text{The time required to accumulate a charge of } 1 \text{ C can then be estimated to be}$ $1 \text{ C} \div (1.6 \times 10^{-10} \text{ C/s}) = 6.25 \times 10^9 \text{ s} = 6.25 \times 10^9 \div (365 \times 24 \times 3600) \text{ years}$ $= 198 \text{ years.}$ $\text{Thus, we will need approximately } 200 \text{ years.}$

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
}