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Current Question (ID: 7493)

Question:

A photon with an initial frequency of $10^{11} \, \text{Hz}$ scatters off an electron at rest. Its final frequency is $0.9 \times 10^{11} \, \text{Hz}$. The speed of scattered electron is close to:

Options:

1. $3 \times 10^2 \, \text{ms}^{-1}$
2. $3.8 \times 10^3 \, \text{ms}^{-1}$
3. $2 \times 10^6 \, \text{ms}^{-1}$
4. $30 \, \text{ms}^{-1}$

Solution:

### **Hint:** Photoelectric effect. **Explanation:** **Step 1:** Apply energy conservation: \[h\nu_1 = h\nu_2 + \frac{1}{2}mv^2\] where $\nu_1$ = initial frequency, $\nu_2$ = final frequency, $m$ = electron mass, $v$ = electron velocity. **Step 2:** Calculate the energy difference: \[\frac{1}{2}mv^2 = h(\nu_1 - \nu_2)\] **Step 3:** Solve for velocity: \[v = \sqrt{\frac{2h(\nu_1 - \nu_2)}{m}}\] **Step 4:** Substitute values: \[v = \sqrt{\frac{2 \times 6.63 \times 10^{-34} \times (10^{11} - 0.9 \times 10^{11})}{9.1 \times 10^{-31}}}\] \[v = \sqrt{14571428} = 3.8 \times 10^3 \, \text{ms}^{-1}\] Thus, the correct answer is $3.8 \times 10^3 \, \text{ms}^{-1}$.

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
}