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A black body has maximum wavelength λₘ at 2000 K. Its corresponding wavelength at 3000 K will be

Asked in CBSE AIPMT 2000 · Wien's law and emissivity

• (1) 3/2λₘ
• (2) 2/3λₘ
• (3) (16)/(81)λₘ
• (4) (81)/(16)λₘ

Step-by-step solution

Why the other options are wrong

• (1) comes from inverting the ratio, (3000)/(2000)=3/2, which would make the hotter body peak at a longer wavelength
• (3) comes from raising the correct ratio to the fourth power, (2/3)⁴=(16)/(81); the fourth power belongs to Stefan's law, while Wien's law is a simple inverse
• (4) comes from the same fourth power applied to the inverted ratio, (3/2)⁴=(81)/(16)

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