Import Question JSON

Current Question (ID: 20886)

Question:

$\text{According to Bohr's theory, what is the angular momentum of an electron located in the fifth orbit?}$

Options:

1. $25 \frac{h}{\pi}$
2. $1.0 \frac{h}{\pi}$
3. $10 \frac{h}{\pi}$
4. $2.5 \frac{h}{\pi}$

Solution:

$\text{Hint: } m_e v r = n \cdot \frac{h}{2\pi} \quad n = 1, 2, 3, \ldots$ $\text{Step 1:}$ $\text{The formula of angular momentum is as follows:}$ $m_e v r = n \cdot \frac{h}{2\pi} \quad n = 1, 2, 3, \ldots$ $\text{Step 2:}$ $\text{For the 5th orbit, } n=5$ $\text{Angular momentum} = 5 \cdot \frac{h}{2\pi}$ $= \frac{2.5h}{\pi}$

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
}