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Current Question (ID: 7526)

Question:

$\text{The wavelength of an electron moving with a velocity of } 2.05 \times 10^7 \text{ m s}^{-1} \text{ would be:}$

Options:

1. $4.65 \times 10^{-12} \text{ m}$
2. $3.55 \times 10^{-11} \text{ m}$
3. $2.34 \times 10^{11} \text{ m}$
4. $6.43 \times 10^{-11} \text{ m}$

Solution:

$\text{HINT: Use de Broglie Equation}$ $\text{STEP 1: Write down de-Broglie Equation}$ $\text{According to de Broglie's equation, } \lambda = \frac{h}{mv}$ $\text{Where, } \lambda = \text{wavelength of moving particle, m = mass of particle, v = velocity of particle, h = Planck's constant.}$ $\text{STEP 2: Substitute the given values in de Broglie Equation.}$ $\text{Given: Mass of an electron} = 9.11 \times 10^{-31} \text{ kg and Velocity (v)} = 2.05 \times 10^7 \text{ m s}^{-1}$ $\text{Substituting the values in the expression of } \lambda:$ $\lambda = \frac{(6.63 \times 10^{-34}) \text{ J s}}{(9.11 \times 10^{-31} \text{ kg})(2.05 \times 10^7 \text{ m s}^{-1})}$ $\lambda = 3.55 \times 10^{-11} \text{ m}$

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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
}