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Current Question (ID: 16614)

Question:

$\text{If a metallic block has no potential difference applied across it, then the mean}$ $\text{velocity of free electron is:}$ $(T = \text{absolute temperature of the block})$

Options:

1. $\text{proportional to } T.$
2. $\text{proportional to } \sqrt{T}$
3. $\text{zero.}$
4. $\text{finite but independent of temperature.}$

Solution:

$\text{In the absence of an external electric field, the mean speed of free electron}$ $\left(v_{\text{rms}}\right)$ $\text{is given by } v_{\text{rms}} = \sqrt{\frac{3KT}{m}} \Rightarrow v_{\text{rms}} \propto \sqrt{T}$ $\text{But the average velocity is zero.}$

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
}