Import Question JSON

Current Question (ID: 20885)

Question:

$\text{The wavelength (in nanometer) associated with a proton moving at } 1.0 \times 10^3 \text{ ms}^{-1} \text{ (Mass of proton = } 1.67 \times 10^{-27} \text{ kg and } h = 6.63 \times 10^{-34} \text{ Js) is:}$

Options:

1. $0.032 \text{ nm}$
2. $0.40 \text{ nm}$
3. $2.50 \text{ nm}$
4. $14.0 \text{ nm}$

Solution:

$\text{Hint: Use DeBroglie wavelength formula}$ $\text{Step 1:}$ $\text{Find the wavelength of the proton using the following formula}$ $\lambda = \frac{h}{m \times v}$ $= \frac{6.63 \times 10^{-34}}{1.67 \times 10^{-27} \times 1 \times 10^3}$ $\lambda = 4.0 \times 10^{-10} \text{ m}$ $\text{Step 2:}$ $\text{Find the answer in nm as follows:}$ $1 \text{ nm} = 10^{-9} \text{ m}$ $\lambda = 4.0 \times 10^{-10} \text{ m}; = 0.4 \text{ nm}$

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
}