Import Question JSON

Current Question (ID: 18336)

Question:

$\text{The half-life of } ^{92}\text{U}_{238} \text{ against } \alpha\text{-decay is } 4.5 \times 10^9 \text{ year. The time taken in a year for the decay of the } \frac{15}{16} \text{ part of this isotope will be:}$

Options:

1. $9.0 \times 10^9$
2. $1.8 \times 10^{10}$
3. $4.5 \times 10^9$
4. $2.7 \times 10^{10}$

Solution:

$\text{Half-life: The time it takes for the concentration of that substance to fall to half of its initial value.}$ $N_0 = 1$ $N = \frac{1}{16}$ $N = \frac{N_0}{2^n} \therefore 2^n = 16 = 2^4$ $\text{Thus, } T = t_{1/2} \times 4 = 4.5 \times 10^9 \times 4 = 1.8 \times 10^{10}$

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
}