Import Question JSON

Current Question (ID: 20898)

Question:

$\text{Electrons are emitted in a cathode ray tube with a velocity of 1000 m/s. Select the correct statement among the following is:}$

Options:

1. $\text{The de Broglie wavelength of an electron is 666.67 nm.}$
2. $\text{The cathode rays travel from the cathode to the anode.}$
3. $\text{The characteristics of electrons depend on the metal used in the cathode.}$
4. $\text{The characteristics of electrons depend on the gas filled inside the cathode tube.}$

Solution:

$\text{Velocity} = 1000 \text{ m/s}$ $\lambda = \frac{h}{mv} = \frac{6.6 \times 10^{-34} \text{ J.s}}{9.1 \times 10^{-31} \text{ kg} \times 10^3}$ $= 725 \times 10^{-9} \text{ m}$ $= 725 \text{ nm}$ $\text{The cathode rays will travel from cathode to the anode.}$ $\text{The characteristics of the electrons does not depend on the nature of the metal of the cathode or the gas filled.}$ $\text{Hence, the correct answer is option (2).}$

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
}