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Current Question (ID: 7514)

Question:

$\text{The energy of an electron in the first Bohr's orbit of an H-atom is -13.6 eV. The possible energy value(s) of the excited state(s) for electrons in Bohr's orbits of hydrogen is (are):}$

Options:

1. $-3.4 \text{ eV}$
2. $-4.2 \text{ eV}$
3. $-6.8 \text{ eV}$
4. $+6.8 \text{ eV}$

Solution:

$\text{Hint: use hydrogen orbital energy formula}$\n\n$E_1 \text{ for } H = -13.6 \text{ eV}; E_n \text{ for } H = \frac{E_1}{n^2};$\n\n$\text{Thus, } E_2 = \frac{-13.6}{4} = -3.4 \text{ eV}; E_3 = \frac{-13.6}{9} = -1.51 \text{ eV};$\n\n$E_4 = \frac{-13.6}{16} = -0.85 \text{ eV } \text{ and so on}$\n\n$\text{When an electron moves to an excited state, it occupies a higher energy level with } n > 1.$\n\n$\text{Looking at our calculated values and comparing with the given options, only } -3.4 \text{ eV (for } n = 2 \text{) appears in the options.}$\n\n$\text{Therefore, the possible energy value of an excited state for electrons in Bohr's orbits of hydrogen is } -3.4 \text{ eV.}$

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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
}