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Current Question (ID: 7535)

Question:

$\text{Consider the following sets of quantum numbers:}$ $\begin{array}{|c|c|c|c|c|} \hline & \text{n} & \text{l} & \text{m} & \text{s} \\ \hline \text{(i)} & 3 & 0 & 0 & +1/2 \\ \hline \text{(ii)} & 2 & 2 & 1 & +1/2 \\ \hline \text{(iii)} & 4 & 3 & -2 & -1/2 \\ \hline \text{(iv)} & 1 & 0 & -1 & -1/2 \\ \hline \text{(v)} & 3 & 2 & 3 & +1/2 \\ \hline \end{array}$ $\text{Which of the following sets of quantum numbers is not possible?}$

Options:

1. $\text{ii, iii and iv}$
2. $\text{i, ii, iii and iv}$
3. $\text{ii, iv and v}$
4. $\text{i and iii}$

Solution:

$\text{Hint: Value of l varies from 0 to n-1}$ $\text{Explanation:}$ $\text{The value of l varies from 0 to n-1 and the value of m varies from -l to +l through zero. The value of 's' } \pm 1/2 \text{ which signifies the spin of an electron. The correct sets of quantum number are the following:}$ $\begin{array}{|c|c|c|c|c|} \hline & \text{n} & \text{l} & \text{m} & \text{s} \\ \hline \text{(ii)} & 2 & 1 & 1 & +1/2 \\ \hline \text{(iv)} & 1 & 0 & 0 & -1/2 \\ \hline \text{(v)} & 3 & 2 & 2 & +1/2 \\ \hline \end{array}$ $\text{Analysis of incorrect sets:}$ $\text{(i) n=3, l=0, m=0, s=+1/2: This is valid as l can be 0 when n=3, and m=0 is within range -l to +l.}$ $\text{(ii) n=2, l=2, m=1, s=+1/2: This is invalid because l cannot be 2 when n=2. Maximum l = n-1 = 1.}$ $\text{(iii) n=4, l=3, m=-2, s=-1/2: This is valid as l can be 3 when n=4, and m=-2 is within range -3 to +3.}$ $\text{(iv) n=1, l=0, m=-1, s=-1/2: This is invalid because when l=0, m can only be 0, not -1.}$ $\text{(v) n=3, l=2, m=3, s=+1/2: This is invalid because when l=2, m can range from -2 to +2, not 3.}$ $\text{Therefore, sets (ii), (iv), and (v) are not possible.}$

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{
  "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
}