Import Question JSON

Current Question (ID: 20894)

Question:

$\text{The shortest wavelength in the Lyman series of H-atom is } \lambda. \text{ and the longest wavelength in the Balmer series of He}^+ \text{ is } \frac{x\lambda}{5}. \text{ The value of } x \text{ is:}$

Options:

1. $7$
2. $11$
3. $13$
4. $9$

Solution:

$\text{The shortest wavelength in Lyman series of H-atom is given}$ $\frac{1}{\lambda} = R_H \left[ \frac{1}{(1)^2} - \frac{1}{(\infty)^2} \right] = R_H$ $\Rightarrow \lambda = \frac{1}{R_H}$ $\text{The longest wavelength in Balmer series He}^+ \text{ ion is given by}$ $\frac{1}{\lambda'} = (2)^2 R_H \left[ \frac{1}{(2)^2} - \frac{1}{(3)^2} \right] = \frac{5R_H}{9}$ $\lambda' = \frac{9}{5R_H} = \frac{9\lambda}{5}$ $\therefore x = 9$

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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
}