Import Question JSON

Current Question (ID: 16784)

Question:

$\text{Ionized hydrogen atoms and } \alpha\text{-particles with the same momenta enter perpendicular to a constant magnetic field, } B. \text{ The ratio of their path radii } r_H : r_\alpha \text{ will be:}$

Options:

1. $1 : 4$
2. $2 : 1$
3. $1 : 2$
4. $4 : 1$

Solution:

$\text{Hint: The radius of the path depends on the charge of the particle.}$ $\text{Step 1: Find the radii of the particles.}$ $r_H = \frac{p}{Bq}$ $r_\alpha = \frac{p}{B(2q)}$ $\text{Step 2: Find the ratio of the radii.}$ $\frac{r_H}{r_\alpha} = \frac{p}{Bq} \times \frac{B(2q)}{p} = \frac{2}{1}$

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
}