KCET · Physics · Thermal Properties of Matter
The surface temperature of the sun which has maximum energy emission at \(500 \mathrm{~nm}\) is \(6000 \mathrm{~K}\). The temperature of a star which has maximum energy emission at \(400 \mathrm{~nm}\) will be
- A \(8500 \mathrm{~K}\)
- B \(4500 \mathrm{~K}\)
- C \(7500 \mathrm{~K}\)
- D \(6500 \mathrm{~K}\)
Answer & Solution
Correct Answer
(C) \(7500 \mathrm{~K}\)
Step-by-step Solution
Detailed explanation
By using Wien's displacement law,
\(\left(\lambda_{m}\right)_{1} T_{1}=\left(\lambda_{m}\right)_{2} T_{2}\)
\(\Rightarrow 500 \times 6000=400 \times T_{2}\)
\(\Rightarrow \quad T_{2}=\frac{500 \times 6000}{400}\)
\(T_{2}=7500 \mathrm{~K}\)
\(\left(\lambda_{m}\right)_{1} T_{1}=\left(\lambda_{m}\right)_{2} T_{2}\)
\(\Rightarrow 500 \times 6000=400 \times T_{2}\)
\(\Rightarrow \quad T_{2}=\frac{500 \times 6000}{400}\)
\(T_{2}=7500 \mathrm{~K}\)
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