Import Question JSON

Current Question (ID: 20890)

Question:

$\text{How many sets of quantum numbers are possible?}$ $\begin{array}{|c|c|c|c|} \hline & n & l & m \\ \hline (a) & 2 & 2 & 1 \\ (b) & 3 & 2 & -2 \\ (c) & 3 & 2 & -1 \\ (d) & 2 & 1 & -1 \\ \hline \end{array}$

Options:

1. $0$
2. $1$
3. $2$
4. $3$

Solution:

$\text{Hint: Azimuthal quantum number } (l) \text{ must satisfy } 0 \leq l < n.$ $\text{To determine how many sets of quantum numbers are valid, we apply the following rules:}$ $1. \text{The principal quantum number } (n) \text{ must be a positive integer.}$ $2. \text{Azimuthal quantum number } (l) \text{ must satisfy } 0 \leq l < n.$ $3. \text{Magnetic quantum number } (m) \text{ must be in the range } -l \leq m \leq l.$ $\text{Analyzing each set:}$ $(a) \ n = 2, \ l = 2, \ m = 1 : \text{Invalid, since } l \text{ must be less than } n.$ $(b) \ n = 3, \ l = 2, \ m = -2 : \text{Valid.}$ $(c) \ n = 3, \ l = 2, \ m = -1 : \text{Valid.}$ $(d) \ n = 2, \ l = 1, \ m = -1 : \text{Valid.}$ $\text{There are 3 valid sets of quantum numbers. So, the correct option is fourth.}$

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
}