Import Question JSON

Current Question (ID: 20896)

Question:

$\text{The speed of an electron in the 7th orbit is } 3.6 \times 10^6 \text{ m/s, the speed in 3rd orbit is-}$

Options:

1. $3.6 \times 10^6 \text{ m/s}$
2. $8.4 \times 10^6 \text{ m/s}$
3. $7.5 \times 10^6 \text{ m/s}$
4. $1.8 \times 10^6 \text{ m/s}$

Solution:

$\text{Speed of electron in } n^{th} \text{ orbit of a Bohr atom is given by}$ $v_n = (v_1)_H \times \frac{Z}{n}$ $\text{If } n = 7$ $v_7 = (v_1)_H \times \frac{Z}{n} = 3.6 \times 10^6 \text{ m/s}$ $\Rightarrow (v_1)_H \times Z = 3.6 \times 10^6 \times 7 \rightarrow \text{Eq-1}$ $\text{If } n = 3$ $v_3 = (v_1)_H \times \frac{Z}{3}$ $\text{Putting value of } (v_1)_H \times Z \text{ from Eq-1}$ $= \frac{7 \times 3.6 \times 10^6}{3}$ $= 8.4 \times 10^6 \text{ m/s}$

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
}