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Question
Find the temperature of a blackbody if its spectrum has a peak at (a) λmax = 700 nm (visible), (b) λmax = 3 cm (microwave region) (c) λmax = 3 m (short radio waves). (Take Wien’s constant b = 2.897 × 10-3 m.K).
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Solution
Given: (a) λmax = 700 nm = 700 × 10-9 m,
(b) λmax = 3 cm = 3 × 10-2 m,
(c) λmax = 3 cm,
b = 2.897 × 10-3 m.K.
∴ λmax T = b
(a) T = `"b"/lambda_"max"`
`= (2.897 xx 10^-3 "m"."K")/(700 xx 10^-9 "m")`
`= (2.897 xx 10^-3)/(7 xx 10^-7)`
= 0.4138 × 104
= 4138 K
(b) T = `"b"/lambda_"max"`
`= (2.897 xx 10^-3 "m"."K")/(3 xx 10^-2 "m")`
`= (2.879 xx 10^-1 "K")/3`
= 0.966 × 10-1 K
= 0.0966 K
(c) T = `"b"/lambda_"max"`
`= (2.897 xx 10^-3 "m.K")/(3 " m")`
= 0.966 × 10-3 K
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