Answer:
(a)
[tex]\lambda _{m}=9.332 \times 10^{-6}m[/tex]
(b)
[tex]\lambda _{m}=1.632 \times 10^{-6}m[/tex]
(c) [tex]\lambda _{m}=4.988 \times 10^{-7}m[/tex]
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Explanation:
According to the Wein's displacement law
[tex]\lambda _{m}\times T = b[/tex]
Where, T be the absolute temperature and b is the Wein's displacement constant.
b = 2.898 x 10^-3 m-K
(a) T = 37°C = 37 + 273 = 310 K
[tex]\lambda _{m}=\frac{b}{T}[/tex]
[tex]\lambda _{m}=\frac{2.893\times 10^{-3}}{310}[/tex]
[tex]\lambda _{m}=9.332 \times 10^{-6}m[/tex]
(b) T = 1500°C = 1500 + 273 = 1773 K
[tex]\lambda _{m}=\frac{b}{T}[/tex]
[tex]\lambda _{m}=\frac{2.893\times 10^{-3}}{1773}[/tex]
[tex]\lambda _{m}=1.632 \times 10^{-6}m[/tex]
(c) T = 5800 K
[tex]\lambda _{m}=\frac{b}{T}[/tex]
[tex]\lambda _{m}=\frac{2.893\times 10^{-3}}{5800}[/tex]
[tex]\lambda _{m}=4.988 \times 10^{-7}m[/tex]
