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Current Question (ID: 20888)

Question:

$\text{The numbers of angular and radial nodes in a 4d orbital are respectively:}$ $\text{1. } 2, 1$ $\text{2. } 1, 2$ $\text{3. } 3, 1$ $\text{4. } 1, 3$

Options:

1. $2, 1$
2. $1, 2$
3. $3, 1$
4. $1, 3$

Solution:

$\text{Hint: The number of radial nodes is given by } (n - l - 1).$ $\text{To find the numbers of angular and radial nodes in a 4d orbital, follow these steps:}$ $(1) \text{ Angular Nodes: The number of angular nodes is given by the azimuthal quantum number } (l)$ $\text{For a d orbital, } l = 2$ $\text{Therefore, a 4d orbital has 2 angular nodes.}$ $(2) \text{ Radial Nodes: The number of radial nodes is given by } n - l - 1, \text{ where } n \text{ is the principal quantum number}$ $\text{For a 4d orbital, } n = 4 \text{ and } l = 2.$ $\text{So, the number of radial nodes is } 4 - 2 - 1 = 1$ $\text{Hence, the numbers of angular and radial nodes in a 4d orbital are respectively } 2 \text{ and } 1.$

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
}