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Current Question (ID: 7488)

Question:

Electrons are emitted with zero velocity from a metal surface when it is exposed to radiation of wavelength $6800$ Å. The work function $(W_0)$ of the metal is:

Options:

1. $3.109 \times 10^{-20} \, \text{J}$
2. $2.922 \times 10^{-19} \, \text{J}$
3. $4.031 \times 10^{19} \, \text{J}$
4. $2.319 \times 10^{-18} \, \text{J}$

Solution:

### Hint: Use the concept on work function and solve the question accordingly **Step 1:** See the relation between supplied energy and work function Work function $(W_0)$ of the metal = $h\nu_0$ Supplied energy $(E) = \text{Work function} + \text{K.E.}$ **Step 2:** Given : $\text{K.E.} = 0$ ; $E = W_0$ \[E = \frac{hc}{\lambda} = W_0\] \[W_0 = \frac{6.6 \times 10^{-34} \times 3 \times 10^8}{6800 \times 10^{-10}} = 2.922 \times 10^{-19} \, \text{J}\]

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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
}