सूर्य विकिरण की तीव्रता 0.49 μm तरंगदैर्ध्य पर अधिकतम है। सूर्य को एक कृष्णिका मानते हुए, सूर्य की अनुमानित कुल उत्सर्जन शक्ति क्या है? [वीन के विस्थापन स्थिरांक = 2890 μm-K पर विचार करें]

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  1. 6.86W/m2
  2. 6.86kW/m2

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Option 1 :
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संकल्पना:

कृष्णिका के लिए स्टीफन-बोल्ट्जमान नियम का उपयोग करना:

\( E = \sigma T^4 \)

तापमान ज्ञात करने के लिए, वीन के नियम को लागू करें:

\( \lambda_{\text{max}} T = b \Rightarrow T = \frac{2890}{0.49} = 5897.96~K \)

अब गणना करें:

\( E = 5.67 \times 10^{-8} \cdot (5897.96)^4 \approx 6.86 \times 10^7~\text{W/m}^2 = 6.86 \times 10^4~\text{kW/m}^2 \)

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