Import Question JSON

Current Question (ID: 20907)

Question:

$\text{Calculate the velocity of the electron in the first orbit of H-atom.}$ $\left(m_e = 9.1 \times 10^{-31} \text{kg}\right)$

Options:

1. $2.18 \times 10^5 \text{ m/s}$
2. $2.18 \times 10^6 \text{ m/s}$
3. $2.18 \times 10^7 \text{ m/s}$
4. $2.18 \times 10^4 \text{ m/s}$

Solution:

$\text{Hint: } mvr = \frac{nh}{2\pi}$ $\text{Step 1: We have to calculate the velocity of the electron in the first orbit of H-atom. The mass of an electron is } 9.1 \times 10^{-31} \text{kg}$ $\text{As we know that, } mvr = \frac{nh}{2\pi}$ $v = \frac{nh}{2\pi \times m \times r}$ $\text{Step 2: } v = \frac{nh}{2\pi \times m \times r}$ $v = \frac{1 \times 6.63 \times 10^{-34} \text{ kg m}^2 \text{ s}^{-1}}{2 \times 3.14 \times 9.11 \times 10^{-31} \text{ kg} \times 0.529 \times 10^{-10} \text{ m}}$ $v = 2.18 \times 10^6 \text{ m/s}$ $\text{Hence, option 2 is the correct answer.}$

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
}