Import Question JSON

Current Question (ID: 7490)

Question:

A photon of wavelength $4 \times 10^{-7}$ m strikes a metal surface, the work function of the metal being 2.13 eV. The kinetic energy of emission would be:

Options:

1. 0.97 eV
2. 97 eV
3. $4.97 \times 10^{-19}$ eV
4. $5.84 \times 10^5$ eV

Solution:

### HINT: Use the general expression of Energy and work function relationship. **Step 1:** \[E = h\nu = h \frac{c}{\lambda}\] \[6.62 \times 10^{-34} \text{ Js} \times 3 \times 10^8 \text{ ms}^{-1} \div 4 \times 10^{-7} \text{ m}\] \[= 4.965 \times 10^{-19} \text{ J}\] **Step 2:** Convert E(J) into E(eV) \[\frac{4.965 \times 10^{-19} \text{ J}}{1.609 \times 10^{-19} \text{ J/eV}} = 3.09 \text{ eV}\] **Step 3:** \[h\nu = h\nu_0 + \frac{1}{2}mv^2\] \[3.09 \text{ eV} = 2.13 \text{ eV} + \text{K.E.}\] \[\text{K.E.} = 3.09 - 2.13 = 0.97 \text{ eV}\] Hence, the correct option is first.

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
}