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Current Question (ID: 20870)

Question:

$\text{The set of a quantum number that represents degenerate orbitals is:}$ $\begin{array}{l} \text{a. } n = 3, \ell = 2, m = 0, s = -\frac{1}{2} \& n = 3, \ell = 2, m = -1, s = +\frac{1}{2} \\ \text{b. } n = 2, \ell = 1, m = 1, s = -\frac{1}{2} \& n = 3, \ell = 1, m = 1, s = +\frac{1}{2} \\ \text{c. } n = 4, \ell = 2, m = -1, s = \frac{1}{2} \& n = 3, \ell = 2, m = -1, s = \frac{1}{2} \end{array}$

Options:

1. $\text{a.}$
2. $\text{b.}$
3. $\text{c.}$
4. $\text{a, b}$

Solution:

$\text{(i) Electron orbitals having the same energy levels are called degenerate orbitals. For degenerate orbitals, the value of } n \text{ and } \ell \text{ are the same respectively.}$ $\text{For example, } 3p \text{ has three degenerate } 3p_x, 3p_y, \text{ and } 3p_z, \text{ and all three orbitals have the same } n \text{ and } \ell \text{ values, that is } n = 3, \text{ and } p = 1.$ $\text{(ii) } n = 3, \ell = 2, m = 0, s = -\frac{1}{2} \& n = 3, \ell = 2, m = -1, s = +\frac{1}{2}$ $\text{Both the orbitals are degenerate because both have the same } n \text{ and } \ell \text{ values, that is } n = 3, \text{ and } \ell = 2$ $\text{Thus, option 1 is the correct answer.}$

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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
}