Import Question JSON

Current Question (ID: 21533)

Question:

$\text{The correct electronic configuration and spin only magnetic moment (BM) of Gd}^{3+} (Z = 64), \text{ respectively, are:}$

Options:

1. $[\text{Xe}] 5f^7 \text{ and } 8.9$
2. $[\text{Xe}] 4f^7 \text{ and } 7.9$
3. $[\text{Xe}] 5f^7 \text{ and } 7.9$
4. $[\text{Xe}] 4f^7 \text{ and } 8.9$

Solution:

$\text{Step 1:}$ $\text{The electronic configuration of Gd is } \text{Xe } 4f^7 5d^1 6s^2$ $\text{Electronic configuration of Gd}^{3+} \text{ is } ^{64}\text{Gd}^{3+} = [\text{Xe}] 4f^7.$ $\text{Step 2:}$ $\text{Gd}^{3+} \text{ having 7 unpaired electrons.}$ $\text{The formula of Magnetic moment}$ $\left( \mu \right) = \sqrt{n(n+2)} \text{ BM}$ $n = \text{Number of unpaired electrons}$ $\mu = \sqrt{7(7+2)} \text{BM}$ $= 7.9 \text{ B. M.}$ $\text{Hence, option 2 is the correct answer.}$

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
}