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Current Question (ID: 20875)

Question:

$\text{A proton and a } \text{Li}^{3+} \text{ nucleus are accelerated by the same potential. If } \lambda_{\text{Li}^{3+}} \text{ and } \lambda_p \text{ denote the de-Broglie wavelengths of } \text{Li}^{3+} \text{ and proton respectively, then the value of } \frac{\lambda_{\text{Li}^{3+}}}{\lambda_p} \text{ is } x \times 10^{-1}. \text{ The value of } x \text{ is:}$ $\text{(Rounded off to the nearest integer)}$ $\text{(Mass of } \text{Li}^{3+} = 8.3 \text{ the mass of a proton)}$

Options:

1. 4
2. 6
3. 2
4. 8

Solution:

$\lambda = \frac{h}{\sqrt{2mqV}}$ $\frac{\lambda_{\text{Li}}}{\lambda_p} = \sqrt{\frac{m_p(e)(v)}{m_{\text{Li}}(3e)(V)}} \quad m_{\text{Li}} = 8.3 \ m_p$ $\frac{\lambda_{\text{Li}}}{\lambda_p} = \sqrt{\frac{1}{8.3 \times 3}} = \frac{1}{5} = 0.2 = 2 \times 10^{-1}$

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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
}