Import Question JSON

Current Question (ID: 18332)

Question:

$\text{A radioactive substance has a rate constant of } 4 \text{ years}^{-1}. \text{ What is its half-life?}$

Options:

1. $0.05 \text{ years}$
2. $0.17 \text{ years}$
3. $0.26 \text{ years}^{-1}$
4. $1.6 \text{ years}$

Solution:

$\text{HINT: Radioactive decay follow first order kinetics.}$ $\text{Explanation: The value of half-life as follows:}$ $t_{1/2} = \frac{0.693}{k}$ $= \frac{0.693}{4 \text{ years}^{-1}}$ $= 0.173 \text{ years (approximately)}$

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
}