Import Question JSON

Current Question (ID: 7580)

Question:

$\text{The circumference of the Bohr orbit for the H atom is related to the de Broglie}$ $\text{wavelength associated with the electron revolving around the orbit by the}$ $\text{following relation:}$

Options:

1. $2\pi r = n\lambda$
2. $\pi r = 2n\lambda$
3. $mvr = n\lambda$
4. $vr = 2n\lambda$

Solution:

$\text{Hint: The circumference of the Bohr orbit for the hydrogen atom is an}$ $\text{integral multiple of the de Broglie wavelength associated with the electron}$ $\text{revolving around the orbit.}$\n\n$\text{STEP 1: Write down the angular momentum of electron according to Bohr's}$ $\text{formula.}$\n\n$\text{We know that, according to Bohr's postulate , the angular momentum is}$ $\text{given by:}$\n\n$mvr = \frac{nh}{2\pi} \text{; where } n = 1, 2, 3... \quad \text{......(1)}$\n\n$\text{STEP 2: Write down de-Broglie's equation}$\n\n$\lambda = \frac{h}{mv} \quad \text{...........(2)}$\n\n$\text{STEP 3: Find the relation between circumference and de - Broglie's}$ $\text{wavelength.}$\n\n$\text{Substituting value of 'mv' from equation(2) to (1)}$\n\n$\frac{hr}{\lambda} = \frac{nh}{2\pi}$\n\n$\Rightarrow 2\pi r = n\lambda$

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
}