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Current Question (ID: 10778)

Question:

$\text{A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at a wavelength of 250 nm is } U_1\text{, at a wavelength of 500 nm is } U_2 \text{ and that at 1000 nm is } U_3\text{. Given Wien's constant } b = 2.88 \times 10^6 \text{ nm-K, which of the following is correct?}$

Options:

1. $U_3 = 0$
2. $U_1 > U_2$
3. $U_2 > U_1$ (Correct)
4. $U_1 = 0$

Solution:

\text{Given: Temperature, } T_1 = 5760\text{K} \text{Since it is given that energy of radiation emitted by the body at:} \text{wavelength 250 nm is } U_1\text{, at wavelength 500 nm is } U_2 \text{, and at 1000 nm is } U_3 \text{According to Wien's law: } \lambda_m T = b \text{where } b = \text{Wien's constant} = 2.88 \times 10^6 \text{ nmK} \text{Therefore: } \lambda_m = \frac{b}{T} \lambda_m = \frac{2.88 \times 10^6 \text{ nmK}}{5760\text{K}} \lambda_m = 500 \text{ nm} \text{Since } \lambda_m \text{ is the wavelength corresponding to maximum energy, } U_2 > U_1

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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
}