Import Question JSON

Current Question (ID: 7527)

Question:

$\text{If the velocity of the electron is } 1.6 \times 10^6 \text{ ms}^{-1}\text{. The de Broglie wavelength associated with this electron is:}$

Options:

1. $590 \text{ pm}$
2. $455 \text{ pm}$
3. $512 \text{ pm}$
4. $401 \text{ pm}$

Solution:

$\text{Hint: } \lambda = \frac{h}{p}$ $\text{Step 1:}$ $\text{From de Broglie's equation}$ $\lambda = \frac{h}{p} = \frac{h}{mv}$ $\text{Step 2:}$ $\lambda = \frac{h}{p} = \frac{h}{mv}$ $\lambda = \frac{6.626 \times 10^{-34} \text{ J s}}{9.11 \times 10^{-31} \text{ kg} \times 1.6 \times 10^6 \text{ (ms)}^{-1}}$ $= 455 \text{ pm}$ $\text{Hence, de Broglie's wavelength associated with the electron is 455 pm.}$

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
}