Import Question JSON

Current Question (ID: 20415)

Question:

$\text{A proton, a deuteron and an } \alpha\text{-particle with the same kinetic energy enter into a uniform magnetic field.}$ $\text{The ratio of the radii of their respective circular paths is:}$

Options:

1. $1 : \sqrt{2} : \sqrt{2}$
2. $1 : 1 : \sqrt{2}$
3. $\sqrt{2} : 1 : 1$
4. $1 : \sqrt{2} : 1$

Solution:

$\text{The radius of the circular path in a magnetic field is given by } r = \frac{\sqrt{2mK}}{qB}.$ $\text{For a proton, deuteron, and } \alpha\text{-particle, the masses are } m_p, 2m_p, \text{ and } 4m_p \text{ respectively,}$ $\text{and charges are } e, e, \text{ and } 2e.$ $\text{Thus, the radii are proportional to } \sqrt{\frac{m}{q}}.$ $\text{Therefore, the ratio is } 1 : \sqrt{2} : 1.$

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
}