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Current Question (ID: 7531)

Question:

$\text{The velocity associated with a proton moving at a potential difference of 1000 V is } 4.37 \times 10^5 \text{ ms}^{-1}\text{. If the hockey ball of mass 0.1 kg is moving with this velocity, then the wavelength associated with this velocity would be:}$

Options:

1. $1.52 \times 10^{-38} \text{ m}$
2. $2.54 \times 10^{-32} \text{ m}$
3. $1.52 \times 10^{-36} \text{ m}$
4. $3.19 \times 10^{-34} \text{ m}$

Solution:

$\text{Hint: } \lambda = \frac{h}{mv}$ $\text{Explanation:}$ $\text{According to de Broglie's equation}$ $\lambda = \frac{h}{mv}$ $\text{Substituting the values in the expression,}$ $\lambda = \frac{6.63 \times 10^{-34} \text{ J s}}{(0.1 \text{ kg})(4.37 \times 10^5 \text{ (ms)}^{-1})} = 1.52 \times 10^{-38} \text{ m}$ $\text{Hence, option 1 is the correct answer.}$

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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
}